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cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">보이기</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_ko.wikipedia.org&uselang=ko" class=""><span>기부</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EA%B3%84%EC%A0%95%EB%A7%8C%EB%93%A4%EA%B8%B0&returnto=%EC%9B%90+%28%EA%B8%B0%ED%95%98%ED%95%99%29" title="계정을 만들고 로그인하는 것이 좋습니다. 하지만 필수는 아닙니다" class=""><span>계정 만들기</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EB%A1%9C%EA%B7%B8%EC%9D%B8&returnto=%EC%9B%90+%28%EA%B8%B0%ED%95%98%ED%95%99%29" title="위키백과에 로그인하면 여러가지 편리한 기능을 사용할 수 있습니다. [o]" accesskey="o" class=""><span>로그인</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="더 많은 옵션" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="개인 도구" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">개인 도구</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="사용자 메뉴" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_ko.wikipedia.org&uselang=ko"><span>기부</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EA%B3%84%EC%A0%95%EB%A7%8C%EB%93%A4%EA%B8%B0&returnto=%EC%9B%90+%28%EA%B8%B0%ED%95%98%ED%95%99%29" title="계정을 만들고 로그인하는 것이 좋습니다. 하지만 필수는 아닙니다"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>계정 만들기</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EB%A1%9C%EA%B7%B8%EC%9D%B8&returnto=%EC%9B%90+%28%EA%B8%B0%ED%95%98%ED%95%99%29" title="위키백과에 로그인하면 여러가지 편리한 기능을 사용할 수 있습니다. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>로그인</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> 로그아웃한 편집자를 위한 문서 <a href="/wiki/%EB%8F%84%EC%9B%80%EB%A7%90:%EC%86%8C%EA%B0%9C" aria-label="편집에 관해 더 알아보기"><span>더 알아보기</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%ED%8A%B9%EC%88%98:%EB%82%B4%EA%B8%B0%EC%97%AC" title="이 IP 주소의 편집 목록 [y]" accesskey="y"><span>기여</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%ED%8A%B9%EC%88%98:%EB%82%B4%EC%82%AC%EC%9A%A9%EC%9E%90%ED%86%A0%EB%A1%A0" title="현재 사용하는 IP 주소에 대한 토론 문서 [n]" accesskey="n"><span>토론</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="사이트"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="목차" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">목차</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">사이드바로 이동</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">숨기기</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">처음 위치</div> </a> </li> <li id="toc-용어" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#용어"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>용어</span> </div> </a> <ul id="toc-용어-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-역사" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#역사"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>역사</span> </div> </a> <ul id="toc-역사-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-해석적_성질" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#해석적_성질"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>해석적 성질</span> </div> </a> <button aria-controls="toc-해석적_성질-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>해석적 성질 하위섹션 토글하기</span> </button> <ul id="toc-해석적_성질-sublist" class="vector-toc-list"> <li id="toc-둘레와_넓이" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#둘레와_넓이"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>둘레와 넓이</span> </div> </a> <ul id="toc-둘레와_넓이-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-방정식" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#방정식"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>방정식</span> </div> </a> <ul id="toc-방정식-sublist" class="vector-toc-list"> <li id="toc-데카르트_좌표계" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#데카르트_좌표계"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.1</span> <span>데카르트 좌표계</span> </div> </a> <ul id="toc-데카르트_좌표계-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-극좌표계" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#극좌표계"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.2</span> <span>극좌표계</span> </div> </a> <ul id="toc-극좌표계-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-복소평면" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#복소평면"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.3</span> <span>복소평면</span> </div> </a> <ul id="toc-복소평면-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-접선의_방정식" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#접선의_방정식"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>접선의 방정식</span> </div> </a> <ul id="toc-접선의_방정식-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-기하적_성질" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#기하적_성질"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>기하적 성질</span> </div> </a> <button aria-controls="toc-기하적_성질-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>기하적 성질 하위섹션 토글하기</span> </button> <ul id="toc-기하적_성질-sublist" class="vector-toc-list"> <li id="toc-대칭" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#대칭"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>대칭</span> </div> </a> <ul id="toc-대칭-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-호와_현" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#호와_현"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>호와 현</span> </div> </a> <ul id="toc-호와_현-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-원과_직선의_위치_관계" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#원과_직선의_위치_관계"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>원과 직선의 위치 관계</span> </div> </a> <ul id="toc-원과_직선의_위치_관계-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-두_원의_위치_관계" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#두_원의_위치_관계"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>두 원의 위치 관계</span> </div> </a> <ul id="toc-두_원의_위치_관계-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-중심각과_원주각" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#중심각과_원주각"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>중심각과 원주각</span> </div> </a> <ul id="toc-중심각과_원주각-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-접선" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#접선"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.6</span> <span>접선</span> </div> </a> <ul id="toc-접선-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-원의_직교" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#원의_직교"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.7</span> <span>원의 직교</span> </div> </a> <ul id="toc-원의_직교-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-작도" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#작도"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>작도</span> </div> </a> <button aria-controls="toc-작도-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>작도 하위섹션 토글하기</span> </button> <ul id="toc-작도-sublist" class="vector-toc-list"> <li id="toc-공선점이_아닌_세_점을_지나는_원" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#공선점이_아닌_세_점을_지나는_원"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>공선점이 아닌 세 점을 지나는 원</span> </div> </a> <ul id="toc-공선점이_아닌_세_점을_지나는_원-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-원의_중심" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#원의_중심"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>원의 중심</span> </div> </a> <ul id="toc-원의_중심-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-원적_문제" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#원적_문제"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>원적 문제</span> </div> </a> <ul id="toc-원적_문제-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-기타_관련_주제" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#기타_관련_주제"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>기타 관련 주제</span> </div> </a> <button aria-controls="toc-기타_관련_주제-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>기타 관련 주제 하위섹션 토글하기</span> </button> <ul id="toc-기타_관련_주제-sublist" class="vector-toc-list"> <li id="toc-내접원,_외접원,_방접원" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#내접원,_외접원,_방접원"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>내접원, 외접원, 방접원</span> </div> </a> <ul id="toc-내접원,_외접원,_방접원-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-문학" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#문학"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>문학</span> </div> </a> <ul id="toc-문학-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-같이_보기" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#같이_보기"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>같이 보기</span> </div> </a> <ul id="toc-같이_보기-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-각주" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#각주"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>각주</span> </div> </a> <ul id="toc-각주-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-외부_링크" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#외부_링크"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>외부 링크</span> </div> </a> <ul id="toc-외부_링크-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="목차" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="목차 토글" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">목차 토글</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">원 (기하학)</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="다른 언어로 문서를 방문합니다. 144개 언어로 읽을 수 있습니다" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-144" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">144개 언어</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Sirkel" title="Sirkel – 아프리칸스어" lang="af" hreflang="af" data-title="Sirkel" data-language-autonym="Afrikaans" data-language-local-name="아프리칸스어" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Kreis_(Geometrie)" title="Kreis (Geometrie) – 독일어(스위스)" lang="gsw" hreflang="gsw" data-title="Kreis (Geometrie)" data-language-autonym="Alemannisch" data-language-local-name="독일어(스위스)" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8A%AD%E1%89%A5" title="ክብ – 암하라어" lang="am" hreflang="am" data-title="ክብ" data-language-autonym="አማርኛ" data-language-local-name="암하라어" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Circumferencia" title="Circumferencia – 아라곤어" lang="an" hreflang="an" data-title="Circumferencia" data-language-autonym="Aragonés" data-language-local-name="아라곤어" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar badge-Q17437796 badge-featuredarticle mw-list-item" title="알찬 글"><a href="https://ar.wikipedia.org/wiki/%D8%AF%D8%A7%D8%A6%D8%B1%D8%A9" title="دائرة – 아랍어" lang="ar" hreflang="ar" data-title="دائرة" data-language-autonym="العربية" data-language-local-name="아랍어" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%AF%D8%A7%D9%8A%D8%B1%D9%87" title="دايره – 이집트 아랍어" lang="arz" hreflang="arz" data-title="دايره" data-language-autonym="مصرى" data-language-local-name="이집트 아랍어" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AC%E0%A7%83%E0%A6%A4%E0%A7%8D%E0%A6%A4" title="বৃত্ত – 아삼어" lang="as" hreflang="as" data-title="বৃত্ত" data-language-autonym="অসমীয়া" data-language-local-name="아삼어" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Circunferencia" title="Circunferencia – 아스투리아어" lang="ast" hreflang="ast" data-title="Circunferencia" data-language-autonym="Asturianu" data-language-local-name="아스투리아어" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-ay mw-list-item"><a href="https://ay.wikipedia.org/wiki/Muyu" title="Muyu – 아이마라어" lang="ay" hreflang="ay" data-title="Muyu" data-language-autonym="Aymar aru" data-language-local-name="아이마라어" class="interlanguage-link-target"><span>Aymar aru</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C3%87evr%C9%99" title="Çevrə – 아제르바이잔어" lang="az" hreflang="az" data-title="Çevrə" data-language-autonym="Azərbaycanca" data-language-local-name="아제르바이잔어" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%AF%D8%A7%DB%8C%D8%B1%D9%87" title="دایره – South Azerbaijani" lang="azb" hreflang="azb" data-title="دایره" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D3%98%D0%B9%D0%BB%D3%99%D0%BD%D3%99" title="Әйләнә – 바슈키르어" lang="ba" hreflang="ba" data-title="Әйләнә" data-language-autonym="Башҡортса" data-language-local-name="바슈키르어" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Apskr%C4%97t%C4%97ms" title="Apskrėtėms – Samogitian" lang="sgs" hreflang="sgs" data-title="Apskrėtėms" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Bilog" title="Bilog – Central Bikol" lang="bcl" hreflang="bcl" data-title="Bilog" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D0%BA%D1%80%D1%83%D0%B6%D0%BD%D0%B0%D1%81%D1%86%D1%8C" title="Акружнасць – 벨라루스어" lang="be" hreflang="be" data-title="Акружнасць" data-language-autonym="Беларуская" data-language-local-name="벨라루스어" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%90%D0%BA%D1%80%D1%83%D0%B6%D1%8B%D0%BD%D0%B0" title="Акружына – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Акружына" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9E%D0%BA%D1%80%D1%8A%D0%B6%D0%BD%D0%BE%D1%81%D1%82" title="Окръжност – 불가리아어" lang="bg" hreflang="bg" data-title="Окръжност" data-language-autonym="Български" data-language-local-name="불가리아어" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A7%83%E0%A6%A4%E0%A7%8D%E0%A6%A4" title="বৃত্ত – 벵골어" lang="bn" hreflang="bn" data-title="বৃত্ত" data-language-autonym="বাংলা" data-language-local-name="벵골어" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%A6%E0%BE%92%E0%BD%BC%E0%BD%A2%E0%BC%8B%E0%BD%90%E0%BD%B2%E0%BD%82%E0%BC%8B" title="སྒོར་ཐིག་ – 티베트어" lang="bo" hreflang="bo" data-title="སྒོར་ཐིག་" data-language-autonym="བོད་ཡིག" data-language-local-name="티베트어" class="interlanguage-link-target"><span>བོད་ཡིག</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Kelc%27h" title="Kelc'h – 브르타뉴어" lang="br" hreflang="br" data-title="Kelc'h" data-language-autonym="Brezhoneg" data-language-local-name="브르타뉴어" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Kru%C5%BEnica" title="Kružnica – 보스니아어" lang="bs" hreflang="bs" data-title="Kružnica" data-language-autonym="Bosanski" data-language-local-name="보스니아어" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Circumfer%C3%A8ncia" title="Circumferència – 카탈로니아어" lang="ca" hreflang="ca" data-title="Circumferència" data-language-autonym="Català" data-language-local-name="카탈로니아어" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A8%D8%A7%D8%B2%D9%86%DB%95_(%D8%A6%DB%95%D9%86%D8%AF%D8%A7%D8%B2%DB%95)" title="بازنە (ئەندازە) – 소라니 쿠르드어" lang="ckb" hreflang="ckb" data-title="بازنە (ئەندازە)" data-language-autonym="کوردی" data-language-local-name="소라니 쿠르드어" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Kru%C5%BEnice" title="Kružnice – 체코어" lang="cs" hreflang="cs" data-title="Kružnice" data-language-autonym="Čeština" data-language-local-name="체코어" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%C3%87%D0%B0%D0%B2%D1%80%D0%B0%D0%BA%C4%83%D1%88" title="Çавракăш – 추바시어" lang="cv" hreflang="cv" data-title="Çавракăш" data-language-autonym="Чӑвашла" data-language-local-name="추바시어" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Cylch" title="Cylch – 웨일스어" lang="cy" hreflang="cy" data-title="Cylch" data-language-autonym="Cymraeg" data-language-local-name="웨일스어" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Cirkel" title="Cirkel – 덴마크어" lang="da" hreflang="da" data-title="Cirkel" data-language-autonym="Dansk" data-language-local-name="덴마크어" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Kreis" title="Kreis – 독일어" lang="de" hreflang="de" data-title="Kreis" data-language-autonym="Deutsch" data-language-local-name="독일어" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-dsb mw-list-item"><a href="https://dsb.wikipedia.org/wiki/Cera_krejza" title="Cera krejza – 저지 소르비아어" lang="dsb" hreflang="dsb" data-title="Cera krejza" data-language-autonym="Dolnoserbski" data-language-local-name="저지 소르비아어" class="interlanguage-link-target"><span>Dolnoserbski</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9A%CF%8D%CE%BA%CE%BB%CE%BF%CF%82" title="Κύκλος – 그리스어" lang="el" hreflang="el" data-title="Κύκλος" data-language-autonym="Ελληνικά" data-language-local-name="그리스어" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/Ser%C4%87_(giometr%C3%ACa)" title="Serć (giometrìa) – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Serć (giometrìa)" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Circle" title="Circle – 영어" lang="en" hreflang="en" data-title="Circle" data-language-autonym="English" data-language-local-name="영어" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Cirklo" title="Cirklo – 에스페란토어" lang="eo" hreflang="eo" data-title="Cirklo" data-language-autonym="Esperanto" data-language-local-name="에스페란토어" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/C%C3%ADrculo" title="Círculo – 스페인어" lang="es" hreflang="es" data-title="Círculo" data-language-autonym="Español" data-language-local-name="스페인어" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Ringjoon" title="Ringjoon – 에스토니아어" lang="et" hreflang="et" data-title="Ringjoon" data-language-autonym="Eesti" data-language-local-name="에스토니아어" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Zirkulu" title="Zirkulu – 바스크어" lang="eu" hreflang="eu" data-title="Zirkulu" data-language-autonym="Euskara" data-language-local-name="바스크어" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa badge-Q17437798 badge-goodarticle mw-list-item" title="좋은 글"><a href="https://fa.wikipedia.org/wiki/%D8%AF%D8%A7%DB%8C%D8%B1%D9%87" title="دایره – 페르시아어" lang="fa" hreflang="fa" data-title="دایره" data-language-autonym="فارسی" data-language-local-name="페르시아어" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Ympyr%C3%A4" title="Ympyrä – 핀란드어" lang="fi" hreflang="fi" data-title="Ympyrä" data-language-autonym="Suomi" data-language-local-name="핀란드어" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Ts%C3%B5%C3%B5rjuun" title="Tsõõrjuun – Võro" lang="vro" hreflang="vro" data-title="Tsõõrjuun" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Iwirini" title="Iwirini – 피지어" lang="fj" hreflang="fj" data-title="Iwirini" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="피지어" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Sirkul" title="Sirkul – 페로어" lang="fo" hreflang="fo" data-title="Sirkul" data-language-autonym="Føroyskt" data-language-local-name="페로어" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Cercle" title="Cercle – 프랑스어" lang="fr" hreflang="fr" data-title="Cercle" data-language-autonym="Français" data-language-local-name="프랑스어" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Kreis_(Geometrii)" title="Kreis (Geometrii) – 북부 프리지아어" lang="frr" hreflang="frr" data-title="Kreis (Geometrii)" data-language-autonym="Nordfriisk" data-language-local-name="북부 프리지아어" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Ciorcal" title="Ciorcal – 아일랜드어" lang="ga" hreflang="ga" data-title="Ciorcal" data-language-autonym="Gaeilge" data-language-local-name="아일랜드어" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E5%9C%93%E5%BD%A2" title="圓形 – 간어" lang="gan" hreflang="gan" data-title="圓形" data-language-autonym="贛語" data-language-local-name="간어" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Serk" title="Serk – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Serk" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Cearcall" title="Cearcall – 스코틀랜드 게일어" lang="gd" hreflang="gd" data-title="Cearcall" data-language-autonym="Gàidhlig" data-language-local-name="스코틀랜드 게일어" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Circunferencia" title="Circunferencia – 갈리시아어" lang="gl" hreflang="gl" data-title="Circunferencia" data-language-autonym="Galego" data-language-local-name="갈리시아어" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%B5%E0%AA%B0%E0%AB%8D%E0%AA%A4%E0%AB%81%E0%AA%B3" title="વર્તુળ – 구자라트어" lang="gu" hreflang="gu" data-title="વર્તુળ" data-language-autonym="ગુજરાતી" data-language-local-name="구자라트어" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Kiarkyl" title="Kiarkyl – 맹크스어" lang="gv" hreflang="gv" data-title="Kiarkyl" data-language-autonym="Gaelg" data-language-local-name="맹크스어" class="interlanguage-link-target"><span>Gaelg</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A2%D7%92%D7%9C" title="מעגל – 히브리어" lang="he" hreflang="he" data-title="מעגל" data-language-autonym="עברית" data-language-local-name="히브리어" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B5%E0%A5%83%E0%A4%A4%E0%A5%8D%E0%A4%A4" title="वृत्त – 힌디어" lang="hi" hreflang="hi" data-title="वृत्त" data-language-autonym="हिन्दी" data-language-local-name="힌디어" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Circle" title="Circle – 피지 힌디어" lang="hif" hreflang="hif" data-title="Circle" data-language-autonym="Fiji Hindi" data-language-local-name="피지 힌디어" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Kru%C5%BEnica" title="Kružnica – 크로아티아어" lang="hr" hreflang="hr" data-title="Kružnica" data-language-autonym="Hrvatski" data-language-local-name="크로아티아어" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hsb mw-list-item"><a href="https://hsb.wikipedia.org/wiki/Kru%C5%BEnica" title="Kružnica – 고지 소르비아어" lang="hsb" hreflang="hsb" data-title="Kružnica" data-language-autonym="Hornjoserbsce" data-language-local-name="고지 소르비아어" class="interlanguage-link-target"><span>Hornjoserbsce</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/S%C3%A8k_(non)" title="Sèk (non) – 아이티어" lang="ht" hreflang="ht" data-title="Sèk (non)" data-language-autonym="Kreyòl ayisyen" data-language-local-name="아이티어" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/K%C3%B6r_(geometria)" title="Kör (geometria) – 헝가리어" lang="hu" hreflang="hu" data-title="Kör (geometria)" data-language-autonym="Magyar" data-language-local-name="헝가리어" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%87%D6%80%D5%BB%D5%A1%D5%B6%D5%A1%D5%A3%D5%AB%D5%AE" title="Շրջանագիծ – 아르메니아어" lang="hy" hreflang="hy" data-title="Շրջանագիծ" data-language-autonym="Հայերեն" data-language-local-name="아르메니아어" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Circulo" title="Circulo – 인터링구아" lang="ia" hreflang="ia" data-title="Circulo" data-language-autonym="Interlingua" data-language-local-name="인터링구아" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Lingkaran" title="Lingkaran – 인도네시아어" lang="id" hreflang="id" data-title="Lingkaran" data-language-autonym="Bahasa Indonesia" data-language-local-name="인도네시아어" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Cirklo" title="Cirklo – 이도어" lang="io" hreflang="io" data-title="Cirklo" data-language-autonym="Ido" data-language-local-name="이도어" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Hringur_(r%C3%BAmfr%C3%A6%C3%B0i)" title="Hringur (rúmfræði) – 아이슬란드어" lang="is" hreflang="is" data-title="Hringur (rúmfræði)" data-language-autonym="Íslenska" data-language-local-name="아이슬란드어" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Circonferenza" title="Circonferenza – 이탈리아어" lang="it" hreflang="it" data-title="Circonferenza" data-language-autonym="Italiano" data-language-local-name="이탈리아어" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%86%86_(%E6%95%B0%E5%AD%A6)" title="円 (数学) – 일본어" lang="ja" hreflang="ja" data-title="円 (数学)" data-language-autonym="日本語" data-language-local-name="일본어" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Soerkl" title="Soerkl – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Soerkl" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Bunderan" title="Bunderan – 자바어" lang="jv" hreflang="jv" data-title="Bunderan" data-language-autonym="Jawa" data-language-local-name="자바어" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%AC%E1%83%A0%E1%83%94%E1%83%AC%E1%83%98%E1%83%A0%E1%83%98" title="წრეწირი – 조지아어" lang="ka" hreflang="ka" data-title="წრეწირი" data-language-autonym="ქართული" data-language-local-name="조지아어" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Tawinest" title="Tawinest – 커바일어" lang="kab" hreflang="kab" data-title="Tawinest" data-language-autonym="Taqbaylit" data-language-local-name="커바일어" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A8%D0%B5%D2%A3%D0%B1%D0%B5%D1%80" title="Шеңбер – 카자흐어" lang="kk" hreflang="kk" data-title="Шеңбер" data-language-autonym="Қазақша" data-language-local-name="카자흐어" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%9A%E1%9E%84%E1%9F%92%E1%9E%9C%E1%9E%84%E1%9F%8B" title="រង្វង់ – 크메르어" lang="km" hreflang="km" data-title="រង្វង់" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="크메르어" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B5%E0%B3%83%E0%B2%A4%E0%B3%8D%E0%B2%A4" title="ವೃತ್ತ – 칸나다어" lang="kn" hreflang="kn" data-title="ವೃತ್ತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="칸나다어" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Gilover" title="Gilover – 쿠르드어" lang="ku" hreflang="ku" data-title="Gilover" data-language-autonym="Kurdî" data-language-local-name="쿠르드어" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Kylgh" title="Kylgh – 콘월어" lang="kw" hreflang="kw" data-title="Kylgh" data-language-autonym="Kernowek" data-language-local-name="콘월어" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%90%D0%B9%D0%BB%D0%B0%D0%BD%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Айлана (математика) – 키르기스어" lang="ky" hreflang="ky" data-title="Айлана (математика)" data-language-autonym="Кыргызча" data-language-local-name="키르기스어" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Circulus" title="Circulus – 라틴어" lang="la" hreflang="la" data-title="Circulus" data-language-autonym="Latina" data-language-local-name="라틴어" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Krees_(Geometrie)" title="Krees (Geometrie) – 룩셈부르크어" lang="lb" hreflang="lb" data-title="Krees (Geometrie)" data-language-autonym="Lëtzebuergesch" data-language-local-name="룩셈부르크어" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Sirculo" title="Sirculo – 링구아 프랑카 노바" lang="lfn" hreflang="lfn" data-title="Sirculo" data-language-autonym="Lingua Franca Nova" data-language-local-name="링구아 프랑카 노바" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Cirkel" title="Cirkel – 림버거어" lang="li" hreflang="li" data-title="Cirkel" data-language-autonym="Limburgs" data-language-local-name="림버거어" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/S%C3%A9rcc" title="Sércc – Lombard" lang="lmo" hreflang="lmo" data-title="Sércc" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Apskritimas" title="Apskritimas – 리투아니아어" lang="lt" hreflang="lt" data-title="Apskritimas" data-language-autonym="Lietuvių" data-language-local-name="리투아니아어" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Ri%C5%86%C4%B7a_l%C4%ABnija" title="Riņķa līnija – 라트비아어" lang="lv" hreflang="lv" data-title="Riņķa līnija" data-language-autonym="Latviešu" data-language-local-name="라트비아어" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Faribolana" title="Faribolana – 말라가시어" lang="mg" hreflang="mg" data-title="Faribolana" data-language-autonym="Malagasy" data-language-local-name="말라가시어" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mhr mw-list-item"><a href="https://mhr.wikipedia.org/wiki/%D0%9E%D2%A5%D0%B3%D0%BE" title="Оҥго – Eastern Mari" lang="mhr" hreflang="mhr" data-title="Оҥго" data-language-autonym="Олык марий" data-language-local-name="Eastern Mari" class="interlanguage-link-target"><span>Олык марий</span></a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Lingkaran" title="Lingkaran – 미낭카바우어" lang="min" hreflang="min" data-title="Lingkaran" data-language-autonym="Minangkabau" data-language-local-name="미낭카바우어" class="interlanguage-link-target"><span>Minangkabau</span></a></li><li class="interlanguage-link interwiki-mk badge-Q17437796 badge-featuredarticle mw-list-item" title="알찬 글"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D1%80%D1%83%D0%B6%D0%BD%D0%B8%D1%86%D0%B0" title="Кружница – 마케도니아어" lang="mk" hreflang="mk" data-title="Кружница" data-language-autonym="Македонски" data-language-local-name="마케도니아어" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B5%E0%B5%83%E0%B4%A4%E0%B5%8D%E0%B4%A4%E0%B4%82" title="വൃത്തം – 말라얄람어" lang="ml" hreflang="ml" data-title="വൃത്തം" data-language-autonym="മലയാളം" data-language-local-name="말라얄람어" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A2%D0%BE%D0%B9%D1%80%D0%BE%D0%B3" title="Тойрог – 몽골어" lang="mn" hreflang="mn" data-title="Тойрог" data-language-autonym="Монгол" data-language-local-name="몽골어" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B5%E0%A4%B0%E0%A5%8D%E0%A4%A4%E0%A5%81%E0%A4%B3" title="वर्तुळ – 마라티어" lang="mr" hreflang="mr" data-title="वर्तुळ" data-language-autonym="मराठी" data-language-local-name="마라티어" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Bulatan" title="Bulatan – 말레이어" lang="ms" hreflang="ms" data-title="Bulatan" data-language-autonym="Bahasa Melayu" data-language-local-name="말레이어" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%85%E1%80%80%E1%80%BA%E1%80%9D%E1%80%AD%E1%80%AF%E1%80%84%E1%80%BA%E1%80%B8" title="စက်ဝိုင်း – 버마어" lang="my" hreflang="my" data-title="စက်ဝိုင်း" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="버마어" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Krink" title="Krink – 저지 독일어" lang="nds" hreflang="nds" data-title="Krink" data-language-autonym="Plattdüütsch" data-language-local-name="저지 독일어" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%B5%E0%A5%83%E0%A4%A4" title="वृत – 네팔어" lang="ne" hreflang="ne" data-title="वृत" data-language-autonym="नेपाली" data-language-local-name="네팔어" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%9A%E0%A4%BE%E0%A4%95%E0%A4%83" title="चाकः – 네와르어" lang="new" hreflang="new" data-title="चाकः" data-language-autonym="नेपाल भाषा" data-language-local-name="네와르어" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Cirkel" title="Cirkel – 네덜란드어" lang="nl" hreflang="nl" data-title="Cirkel" data-language-autonym="Nederlands" data-language-local-name="네덜란드어" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Sirkel" title="Sirkel – 노르웨이어(니노르스크)" lang="nn" hreflang="nn" data-title="Sirkel" data-language-autonym="Norsk nynorsk" data-language-local-name="노르웨이어(니노르스크)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Sirkel" title="Sirkel – 노르웨이어(보크말)" lang="nb" hreflang="nb" data-title="Sirkel" data-language-autonym="Norsk bokmål" data-language-local-name="노르웨이어(보크말)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Cercle" title="Cercle – 오크어" lang="oc" hreflang="oc" data-title="Cercle" data-language-autonym="Occitan" data-language-local-name="오크어" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Geengoo" title="Geengoo – 오로모어" lang="om" hreflang="om" data-title="Geengoo" data-language-autonym="Oromoo" data-language-local-name="오로모어" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%AC%E0%AD%83%E0%AC%A4%E0%AD%8D%E0%AC%A4" title="ବୃତ୍ତ – 오리야어" lang="or" hreflang="or" data-title="ବୃତ୍ତ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="오리야어" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%9A%E0%A9%B1%E0%A8%95%E0%A8%B0" title="ਚੱਕਰ – 펀잡어" lang="pa" hreflang="pa" data-title="ਚੱਕਰ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="펀잡어" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pih mw-list-item"><a href="https://pih.wikipedia.org/wiki/Sirkil" title="Sirkil – Norfuk / Pitkern" lang="pih" hreflang="pih" data-title="Sirkil" data-language-autonym="Norfuk / Pitkern" data-language-local-name="Norfuk / Pitkern" class="interlanguage-link-target"><span>Norfuk / Pitkern</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Okr%C4%85g" title="Okrąg – 폴란드어" lang="pl" hreflang="pl" data-title="Okrąg" data-language-autonym="Polski" data-language-local-name="폴란드어" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%AF%D8%A7%D8%A6%D8%B1%DB%81" title="دائرہ – Western Punjabi" lang="pnb" hreflang="pnb" data-title="دائرہ" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%DA%AF%D8%B1%D8%AF%DA%A9%D9%87" title="گردکه – 파슈토어" lang="ps" hreflang="ps" data-title="گردکه" data-language-autonym="پښتو" data-language-local-name="파슈토어" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Circunfer%C3%AAncia" title="Circunferência – 포르투갈어" lang="pt" hreflang="pt" data-title="Circunferência" data-language-autonym="Português" data-language-local-name="포르투갈어" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/P%27allta_muyu" title="P'allta muyu – 케추아어" lang="qu" hreflang="qu" data-title="P'allta muyu" data-language-autonym="Runa Simi" data-language-local-name="케추아어" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Cerc" title="Cerc – 루마니아어" lang="ro" hreflang="ro" data-title="Cerc" data-language-autonym="Română" data-language-local-name="루마니아어" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-roa-rup mw-list-item"><a href="https://roa-rup.wikipedia.org/wiki/%C8%9Aerc%C4%BEiu" title="Țercľiu – 아로마니아어" lang="rup" hreflang="rup" data-title="Țercľiu" data-language-autonym="Armãneashti" data-language-local-name="아로마니아어" class="interlanguage-link-target"><span>Armãneashti</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9E%D0%BA%D1%80%D1%83%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C" title="Окружность – 러시아어" lang="ru" hreflang="ru" data-title="Окружность" data-language-autonym="Русский" data-language-local-name="러시아어" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%9A%D1%80%D1%83%D0%B3" title="Круг – 루신어" lang="rue" hreflang="rue" data-title="Круг" data-language-autonym="Русиньскый" data-language-local-name="루신어" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Raing" title="Raing – 스코틀랜드어" lang="sco" hreflang="sco" data-title="Raing" data-language-autonym="Scots" data-language-local-name="스코틀랜드어" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%DA%AF%D9%88%D9%84" title="گول – 신디어" lang="sd" hreflang="sd" data-title="گول" data-language-autonym="سنڌي" data-language-local-name="신디어" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Kru%C5%BEnica" title="Kružnica – 세르비아-크로아티아어" lang="sh" hreflang="sh" data-title="Kružnica" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="세르비아-크로아티아어" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Circle" title="Circle – Simple English" lang="en-simple" hreflang="en-simple" data-title="Circle" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Kru%C5%BEnica" title="Kružnica – 슬로바키아어" lang="sk" hreflang="sk" data-title="Kružnica" data-language-autonym="Slovenčina" data-language-local-name="슬로바키아어" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Kro%C5%BEnica" title="Krožnica – 슬로베니아어" lang="sl" hreflang="sl" data-title="Krožnica" data-language-autonym="Slovenščina" data-language-local-name="슬로베니아어" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Denderedzwa" title="Denderedzwa – 쇼나어" lang="sn" hreflang="sn" data-title="Denderedzwa" data-language-autonym="ChiShona" data-language-local-name="쇼나어" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Goobo" title="Goobo – 소말리아어" lang="so" hreflang="so" data-title="Goobo" data-language-autonym="Soomaaliga" data-language-local-name="소말리아어" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Rrethi" title="Rrethi – 알바니아어" lang="sq" hreflang="sq" data-title="Rrethi" data-language-autonym="Shqip" data-language-local-name="알바니아어" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D1%80%D1%83%D0%B6%D0%BD%D0%B8%D1%86%D0%B0" title="Кружница – 세르비아어" lang="sr" hreflang="sr" data-title="Кружница" data-language-autonym="Српски / srpski" data-language-local-name="세르비아어" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Bunderan_(%C3%A9lmu_ukur)" title="Bunderan (élmu ukur) – 순다어" lang="su" hreflang="su" data-title="Bunderan (élmu ukur)" data-language-autonym="Sunda" data-language-local-name="순다어" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Cirkel" title="Cirkel – 스웨덴어" lang="sv" hreflang="sv" data-title="Cirkel" data-language-autonym="Svenska" data-language-local-name="스웨덴어" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Duara" title="Duara – 스와힐리어" lang="sw" hreflang="sw" data-title="Duara" data-language-autonym="Kiswahili" data-language-local-name="스와힐리어" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AE%AE%E0%AF%8D" title="வட்டம் – 타밀어" lang="ta" hreflang="ta" data-title="வட்டம்" data-language-autonym="தமிழ்" data-language-local-name="타밀어" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B5%E0%B1%83%E0%B0%A4%E0%B1%8D%E0%B0%A4%E0%B0%AE%E0%B1%81" title="వృత్తము – 텔루구어" lang="te" hreflang="te" data-title="వృత్తము" data-language-autonym="తెలుగు" data-language-local-name="텔루구어" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A3%E0%B8%B9%E0%B8%9B%E0%B8%A7%E0%B8%87%E0%B8%81%E0%B8%A5%E0%B8%A1" title="รูปวงกลม – 태국어" lang="th" hreflang="th" data-title="รูปวงกลม" data-language-autonym="ไทย" data-language-local-name="태국어" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Bilog" title="Bilog – 타갈로그어" lang="tl" hreflang="tl" data-title="Bilog" data-language-autonym="Tagalog" data-language-local-name="타갈로그어" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C3%87ember" title="Çember – 터키어" lang="tr" hreflang="tr" data-title="Çember" data-language-autonym="Türkçe" data-language-local-name="터키어" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D3%98%D0%B9%D0%BB%D3%99%D0%BD%D3%99" title="Әйләнә – 타타르어" lang="tt" hreflang="tt" data-title="Әйләнә" data-language-autonym="Татарча / tatarça" data-language-local-name="타타르어" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BB%D0%BE" title="Коло – 우크라이나어" lang="uk" hreflang="uk" data-title="Коло" data-language-autonym="Українська" data-language-local-name="우크라이나어" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AF%D8%A7%D8%A6%D8%B1%DB%81" title="دائرہ – 우르두어" lang="ur" hreflang="ur" data-title="دائرہ" data-language-autonym="اردو" data-language-local-name="우르두어" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Aylana" title="Aylana – 우즈베크어" lang="uz" hreflang="uz" data-title="Aylana" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="우즈베크어" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Sercio" title="Sercio – Venetian" lang="vec" hreflang="vec" data-title="Sercio" data-language-autonym="Vèneto" data-language-local-name="Venetian" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%C6%B0%E1%BB%9Dng_tr%C3%B2n" title="Đường tròn – 베트남어" lang="vi" hreflang="vi" data-title="Đường tròn" data-language-autonym="Tiếng Việt" data-language-local-name="베트남어" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Lidong" title="Lidong – 와라이어" lang="war" hreflang="war" data-title="Lidong" data-language-autonym="Winaray" data-language-local-name="와라이어" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%9C%86" title="圆 – 우어" lang="wuu" hreflang="wuu" data-title="圆" data-language-autonym="吴语" data-language-local-name="우어" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/Isazinge" title="Isazinge – 코사어" lang="xh" hreflang="xh" data-title="Isazinge" data-language-autonym="IsiXhosa" data-language-local-name="코사어" class="interlanguage-link-target"><span>IsiXhosa</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A7%D7%A8%D7%99%D7%99%D7%96" title="קרייז – 이디시어" lang="yi" hreflang="yi" data-title="קרייז" data-language-autonym="ייִדיש" data-language-local-name="이디시어" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/%C3%92b%C3%ACr%C3%ADpo" title="Òbìrípo – 요루바어" lang="yo" hreflang="yo" data-title="Òbìrípo" data-language-autonym="Yorùbá" data-language-local-name="요루바어" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-za mw-list-item"><a href="https://za.wikipedia.org/wiki/Luenz" title="Luenz – 주앙어" lang="za" hreflang="za" data-title="Luenz" data-language-autonym="Vahcuengh" data-language-local-name="주앙어" class="interlanguage-link-target"><span>Vahcuengh</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%9C%86" title="圆 – 중국어" lang="zh" hreflang="zh" data-title="圆" data-language-autonym="中文" data-language-local-name="중국어" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E5%9C%93" title="圓 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="圓" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/%C3%8E%E2%81%BF-h%C3%AAng" title="Îⁿ-hêng – 민난어" lang="nan" hreflang="nan" data-title="Îⁿ-hêng" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="민난어" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%9C%93%E5%BD%A2" title="圓形 – 광둥어" lang="yue" hreflang="yue" data-title="圓形" data-language-autonym="粵語" data-language-local-name="광둥어" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q17278#sitelinks-wikipedia" title="언어 간 링크 편집" class="wbc-editpage">링크 편집</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="이름공간"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)" title="본문 보기 [c]" accesskey="c"><span>문서</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a 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hreflang="en"><span>위키미디어 공용</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q17278" title="데이터 저장소에 연결된 항목을 가리키는 링크 [g]" accesskey="g"><span>위키데이터 항목</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="페이지 도구"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="보이기"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">보이기</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">사이드바로 이동</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">숨기기</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">위키백과, 우리 모두의 백과사전.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="ko" dir="ltr"><p><span class="nowrap"></span> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Cercle_noir_100%25.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Cercle_noir_100%25.svg/220px-Cercle_noir_100%25.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Cercle_noir_100%25.svg/330px-Cercle_noir_100%25.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/40/Cercle_noir_100%25.svg/440px-Cercle_noir_100%25.svg.png 2x" data-file-width="512" data-file-height="512" /></a><figcaption>원</figcaption></figure> <p><a href="/wiki/%EA%B8%B0%ED%95%98%ED%95%99" title="기하학">기하학</a>에서 <b>원</b>(圓, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">circle</span>)은 평면 위의 한 <a href="/wiki/%EC%A0%90_(%EA%B8%B0%ED%95%98%ED%95%99)" title="점 (기하학)">점</a>에 이르는 <a href="/wiki/%EA%B1%B0%EB%A6%AC" title="거리">거리</a>가 일정한 <a href="/wiki/%ED%8F%89%EB%A9%B4" title="평면">평면</a> 위의 점들의 <a href="/wiki/%EC%A7%91%ED%95%A9" title="집합">집합</a>으로 정의되는 도형이다. 이러한 점을 원의 <a href="/wiki/%EC%A4%91%EC%8B%AC_(%EA%B8%B0%ED%95%98%ED%95%99)" title="중심 (기하학)">중심</a>이라고 하고, 중심과 원 위의 점을 잇는 선분 또는 이들의 공통된 길이를 원의 <a href="/wiki/%EB%B0%98%EC%A7%80%EB%A6%84" title="반지름">반지름</a>이라고 한다. </p><p>원은 <a href="/wiki/%EC%9D%B4%EC%B0%A8_%EA%B3%A1%EC%84%A0" class="mw-redirect" title="이차 곡선">이차 곡선</a>의 일종인 <a href="/wiki/%ED%83%80%EC%9B%90" title="타원">타원</a>에서 <a href="/wiki/%EC%9D%B4%EC%8B%AC%EB%A5%A0" title="이심률">이심률</a>이 0인 경우이다. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="용어"><span id=".EC.9A.A9.EC.96.B4"></span>용어</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=1" title="부분 편집: 용어"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Circle_lines_2_ko.svg" class="mw-file-description"><img alt="원과 그 위의 반지름, 지름, 현, 호" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Circle_lines_2_ko.svg/220px-Circle_lines_2_ko.svg.png" decoding="async" width="220" height="207" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Circle_lines_2_ko.svg/330px-Circle_lines_2_ko.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Circle_lines_2_ko.svg/440px-Circle_lines_2_ko.svg.png 2x" data-file-width="596" data-file-height="562" /></a><figcaption>현, 지름, 반지름, 할선, 접선</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Circle_slices_2_ko.svg" class="mw-file-description"><img alt="원과 그 위의 호, 활꼴, 부채꼴" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Circle_slices_2_ko.svg/220px-Circle_slices_2_ko.svg.png" decoding="async" width="220" height="209" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Circle_slices_2_ko.svg/330px-Circle_slices_2_ko.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Circle_slices_2_ko.svg/440px-Circle_slices_2_ko.svg.png 2x" data-file-width="507" data-file-height="482" /></a><figcaption>호, 활꼴, 부채꼴</figcaption></figure> <p>원과 관련된 기본적인 용어들은 다음과 같다. </p> <ul><li><b><a href="/wiki/%EB%8B%A8%EC%9C%84%EC%9B%90" title="단위원">단위원</a></b>: 반지름이 1인 원</li> <li><b><a href="/wiki/%EB%8F%99%EC%8B%AC%EC%9B%90" title="동심원">동심원</a></b>: 중심이 같은 두 원</li> <li><b><a href="/wiki/%EB%B0%98%EC%9B%90" title="반원">반원</a></b>: 중심각이 <a href="/wiki/%ED%8F%89%EA%B0%81" title="평각">평각</a>인 부채꼴(활꼴)</li> <li><b><a href="/wiki/%EB%B0%98%EC%A7%80%EB%A6%84" title="반지름">반지름</a></b>: 원의 중심과 그 원 위의 <a href="/wiki/%EC%A0%90" class="mw-disambig" title="점">점</a>을 잇는 <a href="/wiki/%EC%84%A0%EB%B6%84" title="선분">선분</a> 또는 그 선분의 길이. 반지름의 길이는 지름의 2분의 1이다.</li> <li><b><a href="/wiki/%EB%B6%80%EC%B1%84%EA%BC%B4" title="부채꼴">부채꼴</a></b>: 두 개의 반지름과 하나의 호로 둘러싸인 영역</li> <li><b><a href="/wiki/%EC%82%AC%EB%B6%84%EC%9B%90" class="mw-redirect" title="사분원">사분원</a></b>: 중심각이 <a href="/wiki/%EC%A7%81%EA%B0%81" title="직각">직각</a>인 부채꼴</li> <li><b><a href="/wiki/%EC%9B%90%EB%91%98%EB%A0%88" title="원둘레">원주</a></b>: 원의 둘레</li> <li><b><a href="/wiki/%EC%9B%90%EC%A3%BC%EA%B0%81" title="원주각">원주각</a></b>: 한 끝점을 공유하는 두 현이 원 내부에서 이루는 각. 크기는 이에 대응하는 중심각의 1/2이다.</li> <li><b><a href="/wiki/%EC%9B%90%ED%8C%90" title="원판">원판</a></b>: 원으로 둘러싸인 도형</li> <li><b><a href="/w/index.php?title=%EC%9B%90%ED%99%98_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&redlink=1" class="new" title="원환 (기하학) (없는 문서)">원환</a></b>: 두 <a href="/wiki/%EB%8F%99%EC%8B%AC%EC%9B%90" title="동심원">동심원</a>으로 둘러싸인 도형</li> <li><b><a href="/wiki/%EC%A0%91%EC%84%A0" title="접선">접선</a></b>: 원과 한 점에서 만나는 직선</li> <li><b><a href="/wiki/%EC%A0%91%ED%98%84%EA%B0%81" title="접현각">접현각</a></b>: 원의 현과 현의 한 끝점에서의 접선이 이루는 각</li> <li><b><a href="/wiki/%EC%A4%91%EC%8B%AC_(%EA%B8%B0%ED%95%98%ED%95%99)" title="중심 (기하학)">중심</a></b>: 원 위의 임의의 점에 이르는 거리가 일정한 그 원을 포함하는 평면 위의 점</li> <li><b><a href="/wiki/%EC%A4%91%EC%8B%AC%EA%B0%81" title="중심각">중심각</a></b>: 호의 두 끝점을 지나는 반지름이 호와 같은 쪽에서 이루는 각. 크기는 이에 대응하는 원주각의 2배이다.</li> <li><b><a href="/wiki/%EC%A7%80%EB%A6%84" title="지름">지름</a></b>: 원의 중심을 지나는 현 또는 그 길이. 길이는 반지름의 2배이다.</li> <li><b><a href="/w/index.php?title=%EC%BC%A4%EB%A0%88%ED%98%B8&action=edit&redlink=1" class="new" title="켤레호 (없는 문서)">켤레호</a></b>: 원의 합하여 원주 전체를 이루는 두 호</li> <li><b><a href="/wiki/%ED%95%A0%EC%84%A0" title="할선">할선</a></b>: 원과 두 점에서 만나는 직선</li> <li><b><a href="/wiki/%ED%98%84_(%EA%B8%B0%ED%95%98%ED%95%99)" title="현 (기하학)">현</a></b>: 원 위의 두 점을 잇는 선분</li> <li><b><a href="/wiki/%ED%98%B8_(%EA%B8%B0%ED%95%98%ED%95%99)" title="호 (기하학)">호</a></b>: 원의 일부가 되는 곡선</li> <li><b><a href="/wiki/%ED%99%9C%EA%BC%B4" title="활꼴">활꼴</a></b>: 같은 끝점을 갖는 호와 현으로 둘러싸인 영역</li> <li><b><a href="/wiki/%EC%8B%9C_(%EA%B8%B0%ED%95%98%ED%95%99)" title="시 (기하학)">시</a></b>: 할선의 중점을 수선의 발로 하는 선</li></ul> <div style="clear:both;"></div> <div class="mw-heading mw-heading2"><h2 id="역사"><span id=".EC.97.AD.EC.82.AC"></span>역사</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=2" title="부분 편집: 역사"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%EA%B8%B0%EC%9B%90%EC%A0%84_5%EC%84%B8%EA%B8%B0" title="기원전 5세기">기원전 5세기</a>경 <a href="/wiki/%EC%95%88%ED%8B%B0%ED%8F%B0" title="안티폰">안티폰</a>은 <a href="/wiki/%EC%A0%95%EB%8B%A4%EA%B0%81%ED%98%95" title="정다각형">정다각형</a>의 변 수를 계속 늘려가면 결국엔 원이 된다고 생각했다. 이에 15세기 독일의 신학자 <a href="/w/index.php?title=%EC%BF%A0%EC%82%AC%EC%9D%98_%EB%8B%88%EC%BD%9C%EB%9D%BC%EC%9A%B0%EC%8A%A4&action=edit&redlink=1" class="new" title="쿠사의 니콜라우스 (없는 문서)">니콜라우스</a>는 아무리 변을 늘려도 원이 될 수는 없다는 사상으로 반박했다. </p> <div class="mw-heading mw-heading2"><h2 id="해석적_성질"><span id=".ED.95.B4.EC.84.9D.EC.A0.81_.EC.84.B1.EC.A7.88"></span>해석적 성질</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=3" title="부분 편집: 해석적 성질"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="둘레와_넓이"><span id=".EB.91.98.EB.A0.88.EC.99.80_.EB.84.93.EC.9D.B4"></span>둘레와 넓이</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=4" title="부분 편집: 둘레와 넓이"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Circle_area_2_ko.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/67/Circle_area_2_ko.svg/220px-Circle_area_2_ko.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/67/Circle_area_2_ko.svg/330px-Circle_area_2_ko.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/67/Circle_area_2_ko.svg/440px-Circle_area_2_ko.svg.png 2x" data-file-width="562" data-file-height="562" /></a><figcaption>원의 넓이는 색칠된 정사각형의 넓이의 π배이다.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Area_of_a_circle.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Area_of_a_circle.svg/220px-Area_of_a_circle.svg.png" decoding="async" width="220" height="94" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Area_of_a_circle.svg/330px-Area_of_a_circle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Area_of_a_circle.svg/440px-Area_of_a_circle.svg.png 2x" data-file-width="1175" data-file-height="500" /></a><figcaption>반지름의 길이가 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span>인 원은 무한히 작은 부채꼴들로 쪼개어 가로 길이 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7447766f482372c761858f993f1432bd3671b0dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.381ex; height:1.676ex;" alt="{\displaystyle \pi r}"></span>, 세로 길이 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span>의 직사각형으로 만들 수 있다.</figcaption></figure> <p>어떤 원의 반지름의 길이를 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span>라고 하고, 지름의 길이를 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}"></span>라고 하면, 원의 <a href="/wiki/%EB%91%98%EB%A0%88" title="둘레">둘레</a>는 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C=2\pi r=\pi d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mo>=</mo> <mi>π</mi> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C=2\pi r=\pi d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c784450428d0cbe9bcea87111b862f3504e51d5d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:14.054ex; height:2.176ex;" alt="{\displaystyle C=2\pi r=\pi d}"></span></dd></dl> <p>이다. 여기서 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span>는 <a href="/wiki/%EC%9B%90%EC%A3%BC%EC%9C%A8" title="원주율">원주율</a>이다. 이는 약 3.1415…를 값으로 하는 <a href="/wiki/%EC%B4%88%EC%9B%94%EC%88%98" title="초월수">초월수</a>이다. </p><p>어떤 원의 반지름의 길이를 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span>라고 하고, 지름의 길이를 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}"></span>라고 하고, 둘레를 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}"></span>라고 하면, 원(으로 둘러싸인 <a href="/wiki/%EB%8F%84%ED%98%95" title="도형">도형</a>)의 <a href="/wiki/%EB%84%93%EC%9D%B4" title="넓이">넓이</a>는 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A=\pi r^{2}={\frac {\pi d^{2}}{4}}={\frac {C^{2}}{4\pi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>π</mi> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>4</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>4</mn> <mi>π</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=\pi r^{2}={\frac {\pi d^{2}}{4}}={\frac {C^{2}}{4\pi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/756092a411e7a026363fb5be5620fcbb841e9529" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:22.602ex; height:5.676ex;" alt="{\displaystyle A=\pi r^{2}={\frac {\pi d^{2}}{4}}={\frac {C^{2}}{4\pi }}}"></span></dd></dl> <p>이다. <a href="/wiki/%EB%93%B1%EC%A3%BC_%EB%B6%80%EB%93%B1%EC%8B%9D" class="mw-redirect" title="등주 부등식">등주 부등식</a>에 따르면, 이는 둘레가 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}"></span>인 닫힌 곡선으로 둘러싸인 도형이 가질 수 있는 최대 넓이이다. </p> <div style="clear:both;"></div> <div class="mw-heading mw-heading3"><h3 id="방정식"><span id=".EB.B0.A9.EC.A0.95.EC.8B.9D"></span>방정식</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=5" title="부분 편집: 방정식"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="데카르트_좌표계"><span id=".EB.8D.B0.EC.B9.B4.EB.A5.B4.ED.8A.B8_.EC.A2.8C.ED.91.9C.EA.B3.84"></span>데카르트 좌표계</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=6" title="부분 편집: 데카르트 좌표계"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Circle_center_(2,_1)_radius_3.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Circle_center_%282%2C_1%29_radius_3.svg/220px-Circle_center_%282%2C_1%29_radius_3.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Circle_center_%282%2C_1%29_radius_3.svg/330px-Circle_center_%282%2C_1%29_radius_3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/Circle_center_%282%2C_1%29_radius_3.svg/440px-Circle_center_%282%2C_1%29_radius_3.svg.png 2x" data-file-width="562" data-file-height="562" /></a><figcaption>중심이 <span class="nowrap">(2, 1)</span>이고 반지름이 3인 원</figcaption></figure> <p>2차원 <a href="/wiki/%EB%8D%B0%EC%B9%B4%EB%A5%B4%ED%8A%B8_%EC%A2%8C%ED%91%9C%EA%B3%84" title="데카르트 좌표계">데카르트 좌표계</a> 위의 중심이 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (a,b)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (a,b)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7e5710198f33b00695903460983021e75860e2c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.071ex; height:2.843ex;" alt="{\displaystyle (a,b)}"></span>이고 반지름이 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span>인 원의 방정식은 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x-a)^{2}+(y-b)^{2}=r^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mi>a</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <mi>y</mi> <mo>−</mo> <mi>b</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x-a)^{2}+(y-b)^{2}=r^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da8888bb9e8d52fd12fbc05a98715f64c105a884" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.162ex; height:3.176ex;" alt="{\displaystyle (x-a)^{2}+(y-b)^{2}=r^{2}}"></span></dd></dl> <p>이다.<sup id="cite_ref-Gibson_1-0" class="reference"><a href="#cite_note-Gibson-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:22, §3</sup></span> 이는 <a href="/wiki/%ED%94%BC%ED%83%80%EA%B3%A0%EB%9D%BC%EC%8A%A4_%EC%A0%95%EB%A6%AC" title="피타고라스 정리">피타고라스 정리</a>를 통해 유도된다. </p><p>2차원 데카르트 좌표계 위의 원의 방정식의 일반적인 꼴은 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}+y^{2}+dx+ey+f=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>d</mi> <mi>x</mi> <mo>+</mo> <mi>e</mi> <mi>y</mi> <mo>+</mo> <mi>f</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+y^{2}+dx+ey+f=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99d0b0d8746ab7f5665573531334cc83c3ebcf07" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:26.284ex; height:3.009ex;" alt="{\displaystyle x^{2}+y^{2}+dx+ey+f=0}"></span></dd></dl> <p>이다. 단, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d,e,f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>,</mo> <mi>e</mi> <mo>,</mo> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d,e,f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dca5b0133e3a8eacd9e7dd7e8a0b1d0f9b2ce721" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.646ex; height:2.509ex;" alt="{\displaystyle d,e,f}"></span>는 <a href="/wiki/%EC%8B%A4%EC%88%98" title="실수">실수</a>이며, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d^{2}+e^{2}-f>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mi>f</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d^{2}+e^{2}-f>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5daf94dcad6caad44482de8b0d5d506b320a4c95" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.63ex; height:3.009ex;" alt="{\displaystyle d^{2}+e^{2}-f>0}"></span></dd></dl> <p>이어야 한다.<sup id="cite_ref-Gibson_1-1" class="reference"><a href="#cite_note-Gibson-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:23, §3.2</sup></span> 좌변은 반지름의 4배에 대응하며, '=0'일 경우 <a href="/wiki/%ED%95%9C%EC%9B%90%EC%86%8C_%EC%A7%91%ED%95%A9" title="한원소 집합">한원소 집합</a>이 되고, '<0'일 경우 <a href="/wiki/%EA%B3%B5%EC%A7%91%ED%95%A9" title="공집합">공집합</a>이 된다.<sup id="cite_ref-Gibson_1-2" class="reference"><a href="#cite_note-Gibson-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:24, §3.2, Example 3.2</sup></span> </p><p>평면 위의 모든 원은 적절한 데카르트 좌표계를 취했을 때 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}+y^{2}=r^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+y^{2}=r^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37dd4f282df84a83620f71dc52345122e0e3a514" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.64ex; height:3.009ex;" alt="{\displaystyle x^{2}+y^{2}=r^{2}}"></span></dd></dl> <p>와 같은 표준적인 방정식으로 표현된다. 단, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23cbbcd53bd13620bc53490e3eec42790850b452" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.31ex; height:2.176ex;" alt="{\displaystyle r>0}"></span>이어야 한다. 이러한 꼴의 방정식을 얻으려면 원의 중심을 좌표계의 원점으로 삼기만 하면 된다. </p><p>2차원 데카르트 좌표계 위의 중심이 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (a,b)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (a,b)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7e5710198f33b00695903460983021e75860e2c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.071ex; height:2.843ex;" alt="{\displaystyle (a,b)}"></span>이고 반지름이 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span>인 원은 다음과 같은 <a href="/w/index.php?title=%EB%A7%A4%EA%B0%9C%EB%B3%80%EC%88%98_%EB%B0%A9%EC%A0%95%EC%8B%9D&action=edit&redlink=1" class="new" title="매개변수 방정식 (없는 문서)">매개변수 방정식</a>을 갖는다.<sup id="cite_ref-Gibson_1-3" class="reference"><a href="#cite_note-Gibson-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:23, §3.2, (3.5)</sup></span> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{matrix}x=a+r\cos t\\y=b+r\sin t\end{matrix}}\qquad (0\leq t<2\pi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>x</mi> <mo>=</mo> <mi>a</mi> <mo>+</mo> <mi>r</mi> <mi>cos</mi> <mo>⁡</mo> <mi>t</mi> </mtd> </mtr> <mtr> <mtd> <mi>y</mi> <mo>=</mo> <mi>b</mi> <mo>+</mo> <mi>r</mi> <mi>sin</mi> <mo>⁡</mo> <mi>t</mi> </mtd> </mtr> </mtable> </mrow> <mspace width="2em" /> <mo stretchy="false">(</mo> <mn>0</mn> <mo>≤</mo> <mi>t</mi> <mo><</mo> <mn>2</mn> <mi>π</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}x=a+r\cos t\\y=b+r\sin t\end{matrix}}\qquad (0\leq t<2\pi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24042c7f02d9ece6185eba021a200810ddd61708" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:32.171ex; height:6.176ex;" alt="{\displaystyle {\begin{matrix}x=a+r\cos t\\y=b+r\sin t\end{matrix}}\qquad (0\leq t<2\pi )}"></span></dd></dl> <p>여기서 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos ,\sin }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>,</mo> <mi>sin</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos ,\sin }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb709f682d4c55a7ce4af4cbef8aa5da94f4e72b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.001ex; height:2.509ex;" alt="{\displaystyle \cos ,\sin }"></span>은 각각 <a href="/wiki/%EC%BD%94%EC%82%AC%EC%9D%B8_%ED%95%A8%EC%88%98" class="mw-redirect" title="코사인 함수">코사인 함수</a>와 <a href="/wiki/%EC%82%AC%EC%9D%B8_%ED%95%A8%EC%88%98" class="mw-redirect" title="사인 함수">사인 함수</a>이고, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span>는 매개 변수이다. </p> <div class="mw-heading mw-heading4"><h4 id="극좌표계"><span id=".EA.B7.B9.EC.A2.8C.ED.91.9C.EA.B3.84"></span>극좌표계</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=7" title="부분 편집: 극좌표계"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r34311305">.mw-parser-output .hatnote{}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}</style><div role="note" class="hatnote navigation-not-searchable"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Icons8_flat_search.svg/18px-Icons8_flat_search.svg.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Icons8_flat_search.svg/27px-Icons8_flat_search.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/52/Icons8_flat_search.svg/36px-Icons8_flat_search.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span> <a href="/wiki/%EA%B7%B9%EC%A2%8C%ED%91%9C%EA%B3%84#원의_극좌표_방정식" title="극좌표계">극좌표계 § 원의 극좌표 방정식</a> 문서를 참고하십시오.</div> <p>데카르트 좌표 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x,y)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x,y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41cf50e4a314ca8e2c30964baa8d26e5be7a9386" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.328ex; height:2.843ex;" alt="{\displaystyle (x,y)}"></span> 대신 <a href="/wiki/%EA%B7%B9%EC%A2%8C%ED%91%9C" class="mw-redirect" title="극좌표">극좌표</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (r,\theta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>r</mi> <mo>,</mo> <mi>θ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (r,\theta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed8396fdc359fb06c93722137c959e7496e47ed6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.982ex; height:2.843ex;" alt="{\displaystyle (r,\theta )}"></span>를 사용할 수도 있다. 즉, <a href="/wiki/%EA%B7%B9%EC%A2%8C%ED%91%9C%EA%B3%84" title="극좌표계">극좌표계</a> 위의 중심이 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (r_{0},\theta _{0})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (r_{0},\theta _{0})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/081118f53768b7ba0aa01cb89676c270d0d5657a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.091ex; height:2.843ex;" alt="{\displaystyle (r_{0},\theta _{0})}"></span>이고 반지름이 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span>인 원의 방정식은 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r^{2}-2rr_{0}\cos(\theta -\theta _{0})+r_{0}^{2}=R^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>2</mn> <mi>r</mi> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>θ</mi> <mo>−</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>+</mo> <msubsup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r^{2}-2rr_{0}\cos(\theta -\theta _{0})+r_{0}^{2}=R^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99104d7d0dd15a9aba4501d4d22a960be8fc6c8f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:31.5ex; height:3.343ex;" alt="{\displaystyle r^{2}-2rr_{0}\cos(\theta -\theta _{0})+r_{0}^{2}=R^{2}}"></span></dd></dl> <p>이다. </p> <div class="mw-heading mw-heading4"><h4 id="복소평면"><span id=".EB.B3.B5.EC.86.8C.ED.8F.89.EB.A9.B4"></span>복소평면</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=8" title="부분 편집: 복소평면"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>데카르트 좌표나 극좌표를 <a href="/wiki/%EB%B3%B5%EC%86%8C%EC%88%98" title="복소수">복소수</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf368e72c009decd9b6686ee84a375632e11de98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.088ex; height:1.676ex;" alt="{\displaystyle z}"></span>로 대신하면, 원과 <a href="/wiki/%EC%A7%81%EC%84%A0" title="직선">직선</a>의 통일된 방정식을 얻을 수 있다. </p><p><a href="/wiki/%EB%B3%B5%EC%86%8C%ED%8F%89%EB%A9%B4" title="복소평면">복소평면</a> 위에서, 중심이 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e72d1d86e86355892b39b8eb32b964834e113bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.135ex; height:2.009ex;" alt="{\displaystyle z_{0}}"></span>이고 반지름이 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23cbbcd53bd13620bc53490e3eec42790850b452" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.31ex; height:2.176ex;" alt="{\displaystyle r>0}"></span>인 원의 방정식은 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |z-z_{0}|=r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>z</mi> <mo>−</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |z-z_{0}|=r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/463ec9ecfd720ea970063ad16b6b81371eeb2def" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.505ex; height:2.843ex;" alt="{\displaystyle |z-z_{0}|=r}"></span></dd></dl> <p>이다. 여기서 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\cdot |}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\cdot |}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4570d0a1c9fb8f2f413f0b73ce846dd1eb1dca3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.973ex; height:2.843ex;" alt="{\displaystyle |\cdot |}"></span>는 복소수의 <a href="/wiki/%EC%A0%88%EB%8C%93%EA%B0%92" title="절댓값">절댓값</a>이다. </p><p>또한 복소평면 위의 원의 방정식의 일반적인 꼴은 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Az{\bar {z}}+{\bar {B}}z+B{\bar {z}}+C=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>z</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mi>z</mi> <mo>+</mo> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>z</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>+</mo> <mi>C</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Az{\bar {z}}+{\bar {B}}z+B{\bar {z}}+C=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18229c58c21383fc075db2a446eaa10912aff70c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:24.588ex; height:2.676ex;" alt="{\displaystyle Az{\bar {z}}+{\bar {B}}z+B{\bar {z}}+C=0}"></span></dd></dl> <p>이다. 여기서 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow /> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07339d89909a24ef54713d145736261b1fb31123" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0; margin-bottom: -0.338ex; width:1.162ex; height:2.009ex;" alt="{\displaystyle {\bar {}}}"></span>는 <a href="/wiki/%EC%BC%A4%EB%A0%88_%EB%B3%B5%EC%86%8C%EC%88%98" title="켤레 복소수">켤레 복소수</a>이다. 단, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A,C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>,</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A,C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/823f6c4a5d684b894365111fb3429cc9319eb2d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.543ex; height:2.509ex;" alt="{\displaystyle A,C}"></span>는 <a href="/wiki/%EC%8B%A4%EC%88%98" title="실수">실수</a>이고, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span>는 복소수이며, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |B|^{2}-AC>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>B</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mi>A</mi> <mi>C</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |B|^{2}-AC>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b72ee753ddbad56670096412da091fd359158694" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.723ex; height:3.343ex;" alt="{\displaystyle |B|^{2}-AC>0}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\neq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>≠</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\neq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09eef67fa2249348d853a4295747d2d61f759556" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.004ex; height:2.676ex;" alt="{\displaystyle A\neq 0}"></span></dd></dl> <p>이어야 한다. 또한, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\neq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>≠</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\neq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09eef67fa2249348d853a4295747d2d61f759556" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.004ex; height:2.676ex;" alt="{\displaystyle A\neq 0}"></span> 대신 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75c34024483e6fb7c89e45aff3882ebf11d95a00" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.004ex; height:2.176ex;" alt="{\displaystyle A=0}"></span>을 취하고 다른 조건을 그대로 두면 복소평면 위의 직선의 방정식의 일반적인 꼴을 얻는다. 즉, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\neq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>≠</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\neq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09eef67fa2249348d853a4295747d2d61f759556" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.004ex; height:2.676ex;" alt="{\displaystyle A\neq 0}"></span>이라는 조건을 제거하고 다른 조건을 그대로 두면 <a href="/w/index.php?title=%EC%9D%BC%EB%B0%98%ED%99%94_%EC%9B%90&action=edit&redlink=1" class="new" title="일반화 원 (없는 문서)">일반화 원</a>의 방정식의 일반적인 꼴을 얻는다. </p> <div class="mw-heading mw-heading3"><h3 id="접선의_방정식"><span id=".EC.A0.91.EC.84.A0.EC.9D.98_.EB.B0.A9.EC.A0.95.EC.8B.9D"></span>접선의 방정식</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=9" title="부분 편집: 접선의 방정식"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>2차원 데카르트 좌표계 위에서, 원 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x-a)^{2}+(y-b)^{2}=r^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mi>a</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <mi>y</mi> <mo>−</mo> <mi>b</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x-a)^{2}+(y-b)^{2}=r^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da8888bb9e8d52fd12fbc05a98715f64c105a884" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.162ex; height:3.176ex;" alt="{\displaystyle (x-a)^{2}+(y-b)^{2}=r^{2}}"></span></dd></dl> <p>의 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x_{0},y_{0})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x_{0},y_{0})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29c296094af9a1c665425debeac5eaab99a37a04" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.421ex; height:2.843ex;" alt="{\displaystyle (x_{0},y_{0})}"></span>을 접점으로 하는 <a href="/wiki/%EC%A0%91%EC%84%A0" title="접선">접선</a>의 방정식은 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x_{0}-a)(x-a)+(y_{0}-b)(y-b)=r^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>y</mi> <mo>−</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x_{0}-a)(x-a)+(y_{0}-b)(y-b)=r^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e94879c620fa2172e4ff7c0088a1f4770edcb45" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:38.158ex; height:3.176ex;" alt="{\displaystyle (x_{0}-a)(x-a)+(y_{0}-b)(y-b)=r^{2}}"></span></dd></dl> <p>이다. </p><p>원 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x-a)^{2}+(y-b)^{2}=r^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mi>a</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <mi>y</mi> <mo>−</mo> <mi>b</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x-a)^{2}+(y-b)^{2}=r^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da8888bb9e8d52fd12fbc05a98715f64c105a884" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.162ex; height:3.176ex;" alt="{\displaystyle (x-a)^{2}+(y-b)^{2}=r^{2}}"></span></dd></dl> <p>의 기울기가 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span>인 접선의 방정식은 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y-b=m(x-a)\pm r{\sqrt {m^{2}+1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>−</mo> <mi>b</mi> <mo>=</mo> <mi>m</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>±</mo> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>1</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y-b=m(x-a)\pm r{\sqrt {m^{2}+1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae6a41ad9f48e5ec7aa3e72d14f7fcfa8bac5f4d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:30.652ex; height:3.509ex;" alt="{\displaystyle y-b=m(x-a)\pm r{\sqrt {m^{2}+1}}}"></span></dd></dl> <p>이다. </p> <div class="mw-heading mw-heading2"><h2 id="기하적_성질"><span id=".EA.B8.B0.ED.95.98.EC.A0.81_.EC.84.B1.EC.A7.88"></span>기하적 성질</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=10" title="부분 편집: 기하적 성질"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="대칭"><span id=".EB.8C.80.EC.B9.AD"></span>대칭</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=11" title="부분 편집: 대칭"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r27642678/mw-parser-output/.tmulti">.mw-parser-output .tmulti .thumbinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}</style><div class="thumb tmulti tnone"><div class="thumbinner" style="width:682px;max-width:682px"><div class="trow"><div class="tsingle" style="width:358px;max-width:358px"><div class="thumbimage" style="height:242px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Homothetic_centers_of_two_given_nonconcentric_circles.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Homothetic_centers_of_two_given_nonconcentric_circles.svg/356px-Homothetic_centers_of_two_given_nonconcentric_circles.svg.png" decoding="async" width="356" height="242" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Homothetic_centers_of_two_given_nonconcentric_circles.svg/534px-Homothetic_centers_of_two_given_nonconcentric_circles.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Homothetic_centers_of_two_given_nonconcentric_circles.svg/712px-Homothetic_centers_of_two_given_nonconcentric_circles.svg.png 2x" data-file-width="721" data-file-height="491" /></a></span></div></div><div class="tsingle" style="width:320px;max-width:320px"><div class="thumbimage" style="height:242px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Circle_passing_through_three_given_points.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Circle_passing_through_three_given_points.svg/318px-Circle_passing_through_three_given_points.svg.png" decoding="async" width="318" height="243" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Circle_passing_through_three_given_points.svg/477px-Circle_passing_through_three_given_points.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Circle_passing_through_three_given_points.svg/636px-Circle_passing_through_three_given_points.svg.png 2x" data-file-width="643" data-file-height="491" /></a></span></div></div></div></div></div> <ul><li>원은 지름에 대한 <a href="/wiki/%EB%B0%98%EC%82%AC_(%EA%B8%B0%ED%95%98%ED%95%99)" title="반사 (기하학)">반사</a>와 원의 중심에 대한 <a href="/wiki/%ED%9A%8C%EC%A0%84_(%EA%B8%B0%ED%95%98%ED%95%99)" title="회전 (기하학)">회전</a>에 대하여 대칭이다.<sup id="cite_ref-Martin_2-0" class="reference"><a href="#cite_note-Martin-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:227, §20.1, Theorem 20.3</sup></span> <ul><li>즉, 원의 <a href="/w/index.php?title=%EB%8C%80%EC%B9%AD%EA%B5%B0_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&redlink=1" class="new" title="대칭군 (기하학) (없는 문서)">대칭군</a>은 2차원 <a href="/wiki/%EC%A7%81%EA%B5%90%EA%B5%B0" title="직교군">직교군</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {O} (2,\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">O</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {O} (2,\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b6679f051ceca07e43c7cdfe28a7db4c7da5f195" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.492ex; height:2.843ex;" alt="{\displaystyle \operatorname {O} (2,\mathbb {R} )}"></span>이다.</li></ul></li> <li>임의의 두 원은 서로 <a href="/wiki/%EC%A4%91%EC%8B%AC_%EB%8B%AE%EC%9D%8C" class="mw-redirect" title="중심 닮음">중심 닮음</a>이며, <a href="/wiki/%EB%8F%99%EC%8B%AC%EC%9B%90" title="동심원">동심원</a>이 아닐 경우 두 원의 중심을 잇는 선분의 반지름의 비에 따른 내분점 및 외분점을 <a href="/w/index.php?title=%EB%8B%AE%EC%9D%8C_%EC%A4%91%EC%8B%AC&action=edit&redlink=1" class="new" title="닮음 중심 (없는 문서)">닮음 중심</a>으로 갖는다.<sup id="cite_ref-Johnson_3-0" class="reference"><a href="#cite_note-Johnson-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:19, §25</sup></span></li></ul> <ul><li>반지름의 길이가 같은 모든 원은 서로 <a href="/wiki/%ED%95%A9%EB%8F%99_(%EA%B8%B0%ED%95%98%ED%95%99)" title="합동 (기하학)">합동</a>이다.<sup id="cite_ref-Isaacs_4-0" class="reference"><a href="#cite_note-Isaacs-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:23, §1F</sup></span></li> <li><a href="/wiki/%EA%B3%B5%EC%84%A0%EC%A0%90" title="공선점">공선점</a>이 아닌 세 점을 지나는 원은 항상 유일하게 존재한다.<sup id="cite_ref-Isaacs_4-1" class="reference"><a href="#cite_note-Isaacs-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:23, §1F, Theorem 1.15</sup></span> <ul><li>즉, 모든 <a href="/wiki/%EC%82%BC%EA%B0%81%ED%98%95" title="삼각형">삼각형</a>의 <a href="/wiki/%EC%99%B8%EC%A0%91%EC%9B%90" title="외접원">외접원</a>은 유일하게 존재한다.</li> <li>즉, 임의의 세 점을 지나는 <a href="/w/index.php?title=%EC%9D%BC%EB%B0%98%ED%99%94_%EC%9B%90&action=edit&redlink=1" class="new" title="일반화 원 (없는 문서)">일반화 원</a>은 항상 유일하게 존재한다.</li></ul></li></ul> <div class="mw-heading mw-heading3"><h3 id="호와_현"><span id=".ED.98.B8.EC.99.80_.ED.98.84"></span>호와 현</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=12" title="부분 편집: 호와 현"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r27642678/mw-parser-output/.tmulti"><div class="thumb tmulti tnone"><div class="thumbinner" style="width:912px;max-width:912px"><div class="trow"><div class="tsingle" style="width:226px;max-width:226px"><div class="thumbimage" style="height:171px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Perpendicular_bisector_of_a_circle_chord.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Perpendicular_bisector_of_a_circle_chord.svg/224px-Perpendicular_bisector_of_a_circle_chord.svg.png" decoding="async" width="224" height="171" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Perpendicular_bisector_of_a_circle_chord.svg/336px-Perpendicular_bisector_of_a_circle_chord.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Perpendicular_bisector_of_a_circle_chord.svg/448px-Perpendicular_bisector_of_a_circle_chord.svg.png 2x" data-file-width="643" data-file-height="491" /></a></span></div></div><div class="tsingle" style="width:226px;max-width:226px"><div class="thumbimage" style="height:171px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Circle_power_1.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Circle_power_1.svg/224px-Circle_power_1.svg.png" decoding="async" width="224" height="171" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Circle_power_1.svg/336px-Circle_power_1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Circle_power_1.svg/448px-Circle_power_1.svg.png 2x" data-file-width="643" data-file-height="491" /></a></span></div></div><div class="tsingle" style="width:226px;max-width:226px"><div class="thumbimage" style="height:171px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Circle_power_2.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Circle_power_2.svg/224px-Circle_power_2.svg.png" decoding="async" width="224" height="171" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Circle_power_2.svg/336px-Circle_power_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Circle_power_2.svg/448px-Circle_power_2.svg.png 2x" data-file-width="643" data-file-height="491" /></a></span></div></div><div class="tsingle" style="width:226px;max-width:226px"><div class="thumbimage" style="height:171px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Distance_between_a_point_and_a_chord_of_the_circle.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Distance_between_a_point_and_a_chord_of_the_circle.svg/224px-Distance_between_a_point_and_a_chord_of_the_circle.svg.png" decoding="async" width="224" height="171" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Distance_between_a_point_and_a_chord_of_the_circle.svg/336px-Distance_between_a_point_and_a_chord_of_the_circle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/Distance_between_a_point_and_a_chord_of_the_circle.svg/448px-Distance_between_a_point_and_a_chord_of_the_circle.svg.png 2x" data-file-width="643" data-file-height="491" /></a></span></div></div></div></div></div> <ul><li>현의 <a href="/wiki/%EC%88%98%EC%A7%81_%EC%9D%B4%EB%93%B1%EB%B6%84%EC%84%A0" title="수직 이등분선">수직 이등분선</a>은 원의 중심을 지난다.<sup id="cite_ref-Martin_2-1" class="reference"><a href="#cite_note-Martin-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:227, §20.1, Theorem 20.2</sup></span> <ul><li>즉, 현에 수직인 지름은 현을 이등분한다.<sup id="cite_ref-Martin_2-2" class="reference"><a href="#cite_note-Martin-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:227, §20.1, Theorem 20.2</sup></span></li> <li>즉, 지름이 아닌 현을 이등분하는 지름은 현에 수직이다.<sup id="cite_ref-Martin_2-3" class="reference"><a href="#cite_note-Martin-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:227, §20.1, Theorem 20.2</sup></span></li></ul></li> <li>지름은 원의 가장 긴 현이다.<sup id="cite_ref-Isaacs_4-2" class="reference"><a href="#cite_note-Isaacs-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:23, §1F</sup></span></li> <li>(<a href="/wiki/%EB%B0%A9%EB%A9%B1_%EC%A0%95%EB%A6%AC" class="mw-redirect" title="방멱 정리">방멱 정리</a>) 원 위에 있지 않은 점 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span>를 지나는 두 직선 가운데 하나는 원과 점 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>와 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span>에서 만나고, 다른 하나는 원과 점 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}"></span>와 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}"></span>에서 만난다고 하면, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle PA\cdot PB=PC\cdot PD}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mi>A</mi> <mo>⋅</mo> <mi>P</mi> <mi>B</mi> <mo>=</mo> <mi>P</mi> <mi>C</mi> <mo>⋅</mo> <mi>P</mi> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle PA\cdot PB=PC\cdot PD}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf7728250e7f9f94ed380d3527ce1e54be893e12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:20.636ex; height:2.176ex;" alt="{\displaystyle PA\cdot PB=PC\cdot PD}"></span>이다.<sup id="cite_ref-Isaacs_4-3" class="reference"><a href="#cite_note-Isaacs-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:47, §1H, Theorem 1.35</sup></span></li> <li>원 위의 점과 현 사이의 거리와 지름의 곱은 점과 현의 양 끝점 사이의 거리의 곱과 같다.<sup id="cite_ref-Johnson_3-1" class="reference"><a href="#cite_note-Johnson-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:71, §101</sup></span></li></ul> <div class="mw-heading mw-heading3"><h3 id="원과_직선의_위치_관계"><span id=".EC.9B.90.EA.B3.BC_.EC.A7.81.EC.84.A0.EC.9D.98_.EC.9C.84.EC.B9.98_.EA.B4.80.EA.B3.84"></span>원과 직선의 위치 관계</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=13" title="부분 편집: 원과 직선의 위치 관계"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r27642678/mw-parser-output/.tmulti"><div class="thumb tmulti tnone"><div class="thumbinner" style="width:681px;max-width:681px"><div class="trow"><div class="tsingle" style="width:225px;max-width:225px"><div class="thumbimage" style="height:170px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Circle-line_intersection_1.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Circle-line_intersection_1.svg/223px-Circle-line_intersection_1.svg.png" decoding="async" width="223" height="170" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Circle-line_intersection_1.svg/335px-Circle-line_intersection_1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Circle-line_intersection_1.svg/446px-Circle-line_intersection_1.svg.png 2x" data-file-width="643" data-file-height="491" /></a></span></div></div><div class="tsingle" style="width:225px;max-width:225px"><div class="thumbimage" style="height:170px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Circle-line_intersection_2.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Circle-line_intersection_2.svg/223px-Circle-line_intersection_2.svg.png" decoding="async" width="223" height="170" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Circle-line_intersection_2.svg/335px-Circle-line_intersection_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Circle-line_intersection_2.svg/446px-Circle-line_intersection_2.svg.png 2x" data-file-width="643" data-file-height="491" /></a></span></div></div><div class="tsingle" style="width:225px;max-width:225px"><div class="thumbimage" style="height:170px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Circle-line_intersection_3.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Circle-line_intersection_3.svg/223px-Circle-line_intersection_3.svg.png" decoding="async" width="223" height="170" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Circle-line_intersection_3.svg/335px-Circle-line_intersection_3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Circle-line_intersection_3.svg/446px-Circle-line_intersection_3.svg.png 2x" data-file-width="643" data-file-height="491" /></a></span></div></div></div></div></div> <p>평면 위의 원과 직선의 위치 관계는 원의 중심에서 직선까지의 거리 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}"></span>와 원의 반지름 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span>의 대소 관계에 따라 다음과 같은 경우로 나뉜다. </p> <ul><li>만약 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d>r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>></mo> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d>r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cec536c81a7994e4e257932a37384ca59530625" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.363ex; height:2.176ex;" alt="{\displaystyle d>r}"></span>라면, 원과 직선은 만나지 않는다.</li> <li>만약 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d=r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>=</mo> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d=r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21cf89a5a7cb251bc64932aa6bf549ede7e10ff0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.363ex; height:2.176ex;" alt="{\displaystyle d=r}"></span>라면, 원과 직선은 한 점에서 만난다. 즉, 직선은 원의 <a href="/wiki/%EC%A0%91%EC%84%A0" title="접선">접선</a>이다.</li> <li>만약 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d<r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo><</mo> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d<r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b7736b56a7efaa6856ffdb2cb1b8b82361db639" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.363ex; height:2.176ex;" alt="{\displaystyle d<r}"></span>라면, 원과 직선은 두 점에서 만난다. 즉, 직선은 원의 <a href="/wiki/%ED%95%A0%EC%84%A0" title="할선">할선</a>이다.</li></ul> <div class="mw-heading mw-heading3"><h3 id="두_원의_위치_관계"><span id=".EB.91.90_.EC.9B.90.EC.9D.98_.EC.9C.84.EC.B9.98_.EA.B4.80.EA.B3.84"></span>두 원의 위치 관계</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=14" title="부분 편집: 두 원의 위치 관계"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r27642678/mw-parser-output/.tmulti"><div class="thumb tmulti tnone"><div class="thumbinner" style="width:681px;max-width:681px"><div class="trow"><div class="tsingle" style="width:225px;max-width:225px"><div class="thumbimage" style="height:187px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Circle-circle_intersection_1.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Circle-circle_intersection_1.svg/223px-Circle-circle_intersection_1.svg.png" decoding="async" width="223" height="187" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Circle-circle_intersection_1.svg/335px-Circle-circle_intersection_1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Circle-circle_intersection_1.svg/446px-Circle-circle_intersection_1.svg.png 2x" data-file-width="585" data-file-height="491" /></a></span></div></div><div class="tsingle" style="width:225px;max-width:225px"><div class="thumbimage" style="height:187px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Circle-circle_intersection_2.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Circle-circle_intersection_2.svg/223px-Circle-circle_intersection_2.svg.png" decoding="async" width="223" height="187" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Circle-circle_intersection_2.svg/335px-Circle-circle_intersection_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Circle-circle_intersection_2.svg/446px-Circle-circle_intersection_2.svg.png 2x" data-file-width="585" data-file-height="491" /></a></span></div></div><div class="tsingle" style="width:225px;max-width:225px"><div class="thumbimage" style="height:187px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Circle-circle_intersection_3.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Circle-circle_intersection_3.svg/223px-Circle-circle_intersection_3.svg.png" decoding="async" width="223" height="187" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Circle-circle_intersection_3.svg/335px-Circle-circle_intersection_3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Circle-circle_intersection_3.svg/446px-Circle-circle_intersection_3.svg.png 2x" data-file-width="585" data-file-height="491" /></a></span></div></div></div></div></div> <p>두 원의 위치 관계는 두 원의 반지름 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R,r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>,</mo> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R,r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06bb20a122b49cad876a2fb55b141e8ec1b816f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.847ex; height:2.509ex;" alt="{\displaystyle R,r}"></span>와 두 중심 사이의 거리 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}"></span>에 따라 다음과 같은 경우로 나뉜다. </p> <ul><li>만약 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d>R+r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>></mo> <mi>R</mi> <mo>+</mo> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d>R+r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/598e8f4026358b0d63a245b4d16fd09c5dca4702" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.967ex; height:2.343ex;" alt="{\displaystyle d>R+r}"></span>이거나 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d<|R-r|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo><</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>R</mi> <mo>−</mo> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d<|R-r|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0a9e768e9f0890b5240a0752d04fa8919f0fb12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.261ex; height:2.843ex;" alt="{\displaystyle d<|R-r|}"></span>라면, 두 원은 만나지 않는다. <ul><li>만약 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d>R+r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>></mo> <mi>R</mi> <mo>+</mo> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d>R+r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/598e8f4026358b0d63a245b4d16fd09c5dca4702" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.967ex; height:2.343ex;" alt="{\displaystyle d>R+r}"></span>라면, 두 원은 서로의 외부에 놓이며, 교점을 가지지 않는다.</li> <li>만약 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d<|R-r|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo><</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>R</mi> <mo>−</mo> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d<|R-r|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0a9e768e9f0890b5240a0752d04fa8919f0fb12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.261ex; height:2.843ex;" alt="{\displaystyle d<|R-r|}"></span>라면, 작은 원은 큰 원의 내부에 놓이며, 교점을 가지지 않는다.</li></ul></li> <li>만약 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d=R+r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>=</mo> <mi>R</mi> <mo>+</mo> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d=R+r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3976c94c0b3757e834461e0ce7a80a3080ba3dd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.967ex; height:2.343ex;" alt="{\displaystyle d=R+r}"></span>이거나 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d=|R-r|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>R</mi> <mo>−</mo> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d=|R-r|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2dcbe22ee439de8b2e179aa77053235d2ebb09b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.261ex; height:2.843ex;" alt="{\displaystyle d=|R-r|}"></span>라면, 두 원은 한 점에서 만난다. 즉, 두 원은 서로 접한다. <ul><li>만약 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d=R+r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>=</mo> <mi>R</mi> <mo>+</mo> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d=R+r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3976c94c0b3757e834461e0ce7a80a3080ba3dd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.967ex; height:2.343ex;" alt="{\displaystyle d=R+r}"></span>라면, 두 원은 서로의 외부에서 접한다. 즉, 두 원은 외접한다.</li> <li>만약 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d=|R-r|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>R</mi> <mo>−</mo> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d=|R-r|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2dcbe22ee439de8b2e179aa77053235d2ebb09b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.261ex; height:2.843ex;" alt="{\displaystyle d=|R-r|}"></span>라면, 작은 원이 큰 원의 내부에서 큰 원에 접한다. 즉, 두 원은 내접한다.</li></ul></li> <li>만약 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |R-r|<d<R+r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>R</mi> <mo>−</mo> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo><</mo> <mi>d</mi> <mo><</mo> <mi>R</mi> <mo>+</mo> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |R-r|<d<R+r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a88bec1939f7b9d4d6ae42b9a49c26d456441c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.013ex; height:2.843ex;" alt="{\displaystyle |R-r|<d<R+r}"></span>라면, 두 원은 두 점에서 만난다.</li></ul> <div class="mw-heading mw-heading3"><h3 id="중심각과_원주각"><span id=".EC.A4.91.EC.8B.AC.EA.B0.81.EA.B3.BC_.EC.9B.90.EC.A3.BC.EA.B0.81"></span>중심각과 원주각</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=15" title="부분 편집: 중심각과 원주각"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r27642678/mw-parser-output/.tmulti"><div class="thumb tmulti tnone"><div class="thumbinner" style="width:682px;max-width:682px"><div class="trow"><div class="tsingle" style="width:220px;max-width:220px"><div class="thumbimage" style="height:206px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:%EC%A4%91%EC%8B%AC%EA%B0%81%EA%B3%BC%EC%9B%90%EC%A3%BC%EA%B0%81.PNG" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/%EC%A4%91%EC%8B%AC%EA%B0%81%EA%B3%BC%EC%9B%90%EC%A3%BC%EA%B0%81.PNG/218px-%EC%A4%91%EC%8B%AC%EA%B0%81%EA%B3%BC%EC%9B%90%EC%A3%BC%EA%B0%81.PNG" decoding="async" width="218" height="206" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/2/2e/%EC%A4%91%EC%8B%AC%EA%B0%81%EA%B3%BC%EC%9B%90%EC%A3%BC%EA%B0%81.PNG 1.5x" data-file-width="289" data-file-height="273" /></a></span></div></div><div class="tsingle" style="width:212px;max-width:212px"><div class="thumbimage" style="height:206px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:%EC%BC%A4%EB%A0%88%ED%98%B8%EC%9D%98%EC%9B%90%EC%A3%BC%EA%B0%81.PNG" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/1/1a/%EC%BC%A4%EB%A0%88%ED%98%B8%EC%9D%98%EC%9B%90%EC%A3%BC%EA%B0%81.PNG" decoding="async" width="210" height="206" class="mw-file-element" data-file-width="205" data-file-height="201" /></a></span></div></div><div class="tsingle" style="width:244px;max-width:244px"><div class="thumbimage" style="height:206px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:%EB%82%B4%EC%A0%91%EC%82%AC%EA%B0%81%ED%98%95%EC%9D%98%EC%99%B8%EA%B0%81.PNG" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/%EB%82%B4%EC%A0%91%EC%82%AC%EA%B0%81%ED%98%95%EC%9D%98%EC%99%B8%EA%B0%81.PNG/242px-%EB%82%B4%EC%A0%91%EC%82%AC%EA%B0%81%ED%98%95%EC%9D%98%EC%99%B8%EA%B0%81.PNG" decoding="async" width="242" height="206" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/e/e3/%EB%82%B4%EC%A0%91%EC%82%AC%EA%B0%81%ED%98%95%EC%9D%98%EC%99%B8%EA%B0%81.PNG 1.5x" data-file-width="257" data-file-height="219" /></a></span></div></div></div></div></div> <ul><li>주어진 호에 대한 <a href="/wiki/%EC%9B%90%EC%A3%BC%EA%B0%81" title="원주각">원주각</a>의 크기는 그 호에 대한 <a href="/wiki/%EC%A4%91%EC%8B%AC%EA%B0%81" title="중심각">중심각</a>의 1/2이다.<sup id="cite_ref-Isaacs_4-4" class="reference"><a href="#cite_note-Isaacs-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:25, §1F, Theorem 1.16</sup></span></li> <li>같은 호에 대한 두 원주각의 크기는 서로 같다.<sup id="cite_ref-Isaacs_4-5" class="reference"><a href="#cite_note-Isaacs-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:25, §1F</sup></span></li> <li><a href="/w/index.php?title=%EC%BC%A4%EB%A0%88%ED%98%B8&action=edit&redlink=1" class="new" title="켤레호 (없는 문서)">켤레호</a>에 대한 두 중심각은 서로 <a href="/wiki/%EB%B3%B4%EA%B0%81" class="mw-redirect" title="보각">보각</a>이다. <ul><li>즉, <a href="/wiki/%EB%82%B4%EC%A0%91_%EC%82%AC%EA%B0%81%ED%98%95" title="내접 사각형">내접 사각형</a>의 두 대각은 서로 <a href="/wiki/%EB%B3%B4%EA%B0%81" class="mw-redirect" title="보각">보각</a>이다.<sup id="cite_ref-Isaacs_4-6" class="reference"><a href="#cite_note-Isaacs-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:26, §1F, Corollary 1.17</sup></span></li> <li>즉, 내접 사각형의 외각의 크기는 <a href="/w/index.php?title=%EB%82%B4%EB%8C%80%EA%B0%81&action=edit&redlink=1" class="new" title="내대각 (없는 문서)">내대각</a>과 같다.</li></ul></li></ul> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r27642678/mw-parser-output/.tmulti"><div class="thumb tmulti tnone"><div class="thumbinner" style="width:512px;max-width:512px"><div class="trow"><div class="tsingle" style="width:247px;max-width:247px"><div class="thumbimage" style="height:244px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:%EC%A7%80%EB%A6%84%EC%9D%98%EC%9B%90%EC%A3%BC%EA%B0%81.PNG" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/7/73/%EC%A7%80%EB%A6%84%EC%9D%98%EC%9B%90%EC%A3%BC%EA%B0%81.PNG" decoding="async" width="245" height="245" class="mw-file-element" data-file-width="215" data-file-height="215" /></a></span></div></div><div class="tsingle" style="width:261px;max-width:261px"><div class="thumbimage" style="height:244px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:%EC%A0%91%EC%84%A0%EA%B3%BC%EC%9B%90%EC%A3%BC%EA%B0%81.PNG" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/%EC%A0%91%EC%84%A0%EA%B3%BC%EC%9B%90%EC%A3%BC%EA%B0%81.PNG/259px-%EC%A0%91%EC%84%A0%EA%B3%BC%EC%9B%90%EC%A3%BC%EA%B0%81.PNG" decoding="async" width="259" height="244" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/f/f5/%EC%A0%91%EC%84%A0%EA%B3%BC%EC%9B%90%EC%A3%BC%EA%B0%81.PNG 1.5x" data-file-width="266" data-file-height="251" /></a></span></div></div></div></div></div> <ul><li>(<a href="/wiki/%ED%83%88%EB%A0%88%EC%8A%A4_%EC%A0%95%EB%A6%AC_(%EC%A7%80%EB%A6%84)" title="탈레스 정리 (지름)">탈레스 정리</a>) 지름에 대한 원주각은 직각이다. <ul><li>즉, 삼각형의 <a href="/wiki/%EC%99%B8%EC%8B%AC" class="mw-redirect" title="외심">외심</a>이 변 위에 있을 필요충분조건은 <a href="/wiki/%EC%A7%81%EA%B0%81_%EC%82%BC%EA%B0%81%ED%98%95" class="mw-redirect" title="직각 삼각형">직각 삼각형</a>이다.<sup id="cite_ref-Isaacs_4-7" class="reference"><a href="#cite_note-Isaacs-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:30, §1F, Corollary 1.22</sup></span></li></ul></li> <li>원의 두 현이 원 내부에서 이루는 각의 크기는 이 각과 <a href="/wiki/%EB%A7%9E%EA%BC%AD%EC%A7%80%EA%B0%81" title="맞꼭지각">맞꼭지각</a>의 내부에 포함되는 두 호에 대한 중심각의 합의 1/2이다.<sup id="cite_ref-Isaacs_4-8" class="reference"><a href="#cite_note-Isaacs-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:27, §1F, Corollary 1.19</sup></span></li> <li>원의 두 할선이 원 외부에서 이루는 각의 크기는 이 각의 내부에 포함되는 두 호에 대한 중심각의 차의 1/2이다.<sup id="cite_ref-Isaacs_4-9" class="reference"><a href="#cite_note-Isaacs-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:27, §1F, Corollary 1.18</sup></span></li></ul> <div class="mw-heading mw-heading3"><h3 id="접선"><span id=".EC.A0.91.EC.84.A0"></span>접선</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=16" title="부분 편집: 접선"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r27642678/mw-parser-output/.tmulti"><div class="thumb tmulti tnone"><div class="thumbinner" style="width:682px;max-width:682px"><div class="trow"><div class="tsingle" style="width:290px;max-width:290px"><div class="thumbimage" style="height:269px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:%EB%B0%98%EC%A7%80%EB%A6%84%EA%B3%BC%EC%A0%91%EC%84%A0%EC%9D%98%EA%B0%81.PNG" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/%EB%B0%98%EC%A7%80%EB%A6%84%EA%B3%BC%EC%A0%91%EC%84%A0%EC%9D%98%EA%B0%81.PNG/288px-%EB%B0%98%EC%A7%80%EB%A6%84%EA%B3%BC%EC%A0%91%EC%84%A0%EC%9D%98%EA%B0%81.PNG" decoding="async" width="288" height="270" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/a/a1/%EB%B0%98%EC%A7%80%EB%A6%84%EA%B3%BC%EC%A0%91%EC%84%A0%EC%9D%98%EA%B0%81.PNG 1.5x" data-file-width="314" data-file-height="294" /></a></span></div></div><div class="tsingle" style="width:388px;max-width:388px"><div class="thumbimage" style="height:269px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:%ED%98%84%EA%B3%BC%EB%B9%84%EB%A1%802.PNG" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/2/27/%ED%98%84%EA%B3%BC%EB%B9%84%EB%A1%802.PNG" decoding="async" width="386" height="270" class="mw-file-element" data-file-width="372" data-file-height="260" /></a></span></div></div></div></div></div> <ul><li>원 위의 한 점을 지나는 원의 접선은 유일하게 존재하고, 이는 이 점을 지나는 반지름에 수직이다.<sup id="cite_ref-Martin_2-4" class="reference"><a href="#cite_note-Martin-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:228, §20.1, Theorem 20.4</sup></span><sup id="cite_ref-Isaacs_4-10" class="reference"><a href="#cite_note-Isaacs-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:30-31, §1F</sup></span> <ul><li>즉, 반지름의 반지름 끝점에서의 수선은 원에 접한다.<sup id="cite_ref-Martin_2-5" class="reference"><a href="#cite_note-Martin-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:228, §20.1, Theorem 20.4</sup></span></li> <li>즉, 원의 접선의 접점에서의 수선은 원의 중심을 지난다.</li></ul></li> <li>원 외부의 한 점을 지나는 원의 접선은 정확히 2개이고, 이 점과 두 접점 사이의 거리는 같으며, 두 접선이 이루는 각과 두 접점을 지나는 반지름이 이루는 각은 서로 보각이다.</li> <li>원의 <a href="/wiki/%EC%A0%91%ED%98%84%EA%B0%81" title="접현각">접현각</a>의 크기는 현을 기준으로 이와 같은 쪽에 있는 호에 대한 중심각의 1/2이다.<sup id="cite_ref-Isaacs_4-11" class="reference"><a href="#cite_note-Isaacs-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:31, §1F, Theorem 1.23</sup></span></li> <li>원의 접선과 할선이 원 외부에서 이루는 각은 각의 내부에 포함된 두 호의 중심각의 차의 1/2이다.<sup id="cite_ref-Isaacs_4-12" class="reference"><a href="#cite_note-Isaacs-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:31, §1F, Corollary 1.24</sup></span></li> <li>외접하는 두 원의 교점을 지나는 두 공통 할선 사이의 두 현은 서로 <a href="/wiki/%ED%8F%89%ED%96%89" title="평행">평행</a>한다.<sup id="cite_ref-Isaacs_4-13" class="reference"><a href="#cite_note-Isaacs-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:31, §1F, Problem 1.25</sup></span></li> <li>(접선에 대한 <a href="/wiki/%EB%B0%A9%EB%A9%B1_%EC%A0%95%EB%A6%AC" class="mw-redirect" title="방멱 정리">방멱 정리</a>)원 외부의 점 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span>를 지나는 두 직선 가운데 하나는 원과 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>와 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span>에서 만나고, 하나는 원에 점 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span>에서 접한다고 하면, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle PA\cdot PB=PT^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mi>A</mi> <mo>⋅</mo> <mi>P</mi> <mi>B</mi> <mo>=</mo> <mi>P</mi> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle PA\cdot PB=PT^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/764bda769ea31dce92930fa7833f67e0e19d045a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:16.295ex; height:2.676ex;" alt="{\displaystyle PA\cdot PB=PT^{2}}"></span>이다.</li></ul> <div class="mw-heading mw-heading3"><h3 id="원의_직교"><span id=".EC.9B.90.EC.9D.98_.EC.A7.81.EA.B5.90"></span>원의 직교</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=17" title="부분 편집: 원의 직교"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>두 원의 교점에서의 두 접선이 서로 <a href="/wiki/%EC%88%98%EC%A7%81" class="mw-redirect" title="수직">수직</a>일 경우 두 원이 서로 <a href="/wiki/%EC%A7%81%EA%B5%90" title="직교">직교</a>한다고 한다.<sup id="cite_ref-Johnson_3-2" class="reference"><a href="#cite_note-Johnson-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:33, §48</sup></span></li> <li>두 원의 반지름이 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r,r'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>,</mo> <msup> <mi>r</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r,r'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/179e9475ca1b29a7c61b5c18fe65dfcce08dd3ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.816ex; height:2.843ex;" alt="{\displaystyle r,r'}"></span>이고, 두 중심 사이의 거리가 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}"></span>라고 할 때, 두 원이 서로 직교할 필요충분조건은 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r^{2}+{r'}^{2}=d^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>r</mi> <mo>′</mo> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r^{2}+{r'}^{2}=d^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eca8f51689f1944eb085780790db0a42ffc5c83f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:13.102ex; height:3.176ex;" alt="{\displaystyle r^{2}+{r'}^{2}=d^{2}}"></span>이다.<sup id="cite_ref-Johnson_3-3" class="reference"><a href="#cite_note-Johnson-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:34, §48</sup></span></li> <li>주어진 원에 직교하고 중심이 원 외부의 주어진 점인 원은 유일하게 존재한다.<sup id="cite_ref-Johnson_3-4" class="reference"><a href="#cite_note-Johnson-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:34, §48</sup></span></li> <li>주어진 원에 직교하고 원의 지름이 아닌 현의 두 끝점을 지나는 원은 유일하게 존재한다.<sup id="cite_ref-Johnson_3-5" class="reference"><a href="#cite_note-Johnson-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:34, §48</sup></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="작도"><span id=".EC.9E.91.EB.8F.84"></span>작도</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=18" title="부분 편집: 작도"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="공선점이_아닌_세_점을_지나는_원"><span id=".EA.B3.B5.EC.84.A0.EC.A0.90.EC.9D.B4_.EC.95.84.EB.8B.8C_.EC.84.B8_.EC.A0.90.EC.9D.84_.EC.A7.80.EB.82.98.EB.8A.94_.EC.9B.90"></span>공선점이 아닌 세 점을 지나는 원</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=19" title="부분 편집: 공선점이 아닌 세 점을 지나는 원"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>공선점이 아닌 세 점 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A,B,C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>,</mo> <mi>B</mi> <mo>,</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A,B,C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ce2acf22b93dfbd22373336bd9c22dbd98a49d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.341ex; height:2.509ex;" alt="{\displaystyle A,B,C}"></span>를 지나는 원은 컴퍼스와 자를 사용하여 다음과 같이 <a href="/wiki/%EC%9E%91%EB%8F%84" class="mw-redirect" title="작도">작도</a>할 수 있다. </p> <ul><li>선분 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle AB}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle AB}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b04153f9681e5b06066357774475c04aaef3a8bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.507ex; height:2.176ex;" alt="{\displaystyle AB}"></span>의 <a href="/wiki/%EC%88%98%EC%A7%81_%EC%9D%B4%EB%93%B1%EB%B6%84%EC%84%A0" title="수직 이등분선">수직 이등분선</a>을 그린다.</li> <li>선분 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle BC}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle BC}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74e0f24a49061dcd63874f7d81f395b5f38800f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.53ex; height:2.176ex;" alt="{\displaystyle BC}"></span>의 수직 이등분선을 그린다.</li> <li>선분 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle AB}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle AB}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b04153f9681e5b06066357774475c04aaef3a8bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.507ex; height:2.176ex;" alt="{\displaystyle AB}"></span>와 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle BC}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle BC}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74e0f24a49061dcd63874f7d81f395b5f38800f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.53ex; height:2.176ex;" alt="{\displaystyle BC}"></span>의 교점 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.773ex; height:2.176ex;" alt="{\displaystyle O}"></span>를 취한다.</li> <li>점 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.773ex; height:2.176ex;" alt="{\displaystyle O}"></span>를 중심으로 하고 선분 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle OA}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle OA}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db864cf94e2655d6a7b56c7479f63933e97afb06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.516ex; height:2.176ex;" alt="{\displaystyle OA}"></span>를 반지름으로 하는 원을 그린다. 이 경우 원은 점 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A,B,C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>,</mo> <mi>B</mi> <mo>,</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A,B,C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ce2acf22b93dfbd22373336bd9c22dbd98a49d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.341ex; height:2.509ex;" alt="{\displaystyle A,B,C}"></span>를 지난다.</li></ul> <div class="mw-heading mw-heading3"><h3 id="원의_중심"><span id=".EC.9B.90.EC.9D.98_.EC.A4.91.EC.8B.AC"></span>원의 중심</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=20" title="부분 편집: 원의 중심"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>주어진 원의 중심은 컴퍼스와 자를 사용하여 다음과 같이 작도할 수 있다. </p> <ul><li>원 위의 두 점 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A,B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>,</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A,B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96c3298ea9aa77c226be56a7d8515baaa517b90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.541ex; height:2.509ex;" alt="{\displaystyle A,B}"></span>을 취한다.</li> <li>선분 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle AB}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle AB}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b04153f9681e5b06066357774475c04aaef3a8bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.507ex; height:2.176ex;" alt="{\displaystyle AB}"></span>의 점 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span>에서의 수선 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle BP}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle BP}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d10edbefafdfad44a1cec72a3cd172ec539f36eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.509ex; height:2.176ex;" alt="{\displaystyle BP}"></span>를 그린다.</li> <li>직선 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle BP}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle BP}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d10edbefafdfad44a1cec72a3cd172ec539f36eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.509ex; height:2.176ex;" alt="{\displaystyle BP}"></span>와 원의 교점 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}"></span>를 취한다. 이 경우 선분 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle AC}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle AC}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b930d133ca536a071bec52a9acc4b05482890d53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.509ex; height:2.176ex;" alt="{\displaystyle AC}"></span>는 원의 지름이다.</li> <li>또 다른 지름 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A'C'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mo>′</mo> </msup> <msup> <mi>C</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A'C'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46480381f20bf3a55d0ba51ec4f836903faca314" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.91ex; height:2.509ex;" alt="{\displaystyle A'C'}"></span>을 작도한다.</li> <li>선분 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle AC}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle AC}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b930d133ca536a071bec52a9acc4b05482890d53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.509ex; height:2.176ex;" alt="{\displaystyle AC}"></span>와 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A'C'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mo>′</mo> </msup> <msup> <mi>C</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A'C'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46480381f20bf3a55d0ba51ec4f836903faca314" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.91ex; height:2.509ex;" alt="{\displaystyle A'C'}"></span>의 교점 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.773ex; height:2.176ex;" alt="{\displaystyle O}"></span>를 취한다. 이 경우 점 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.773ex; height:2.176ex;" alt="{\displaystyle O}"></span>는 원의 중심이다.</li></ul> <div class="mw-heading mw-heading3"><h3 id="원적_문제"><span id=".EC.9B.90.EC.A0.81_.EB.AC.B8.EC.A0.9C"></span>원적 문제</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=21" title="부분 편집: 원적 문제"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r34311305"><div role="note" class="hatnote navigation-not-searchable"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Icons8_flat_search.svg/18px-Icons8_flat_search.svg.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Icons8_flat_search.svg/27px-Icons8_flat_search.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/52/Icons8_flat_search.svg/36px-Icons8_flat_search.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span> 이 부분의 본문은 <a href="/wiki/%EC%9B%90%EC%A0%81_%EB%AC%B8%EC%A0%9C" title="원적 문제">원적 문제</a>입니다.</div> <p><a href="/wiki/%EC%9B%90%EC%A0%81_%EB%AC%B8%EC%A0%9C" title="원적 문제">원적 문제</a>는 주어진 원과 넓이가 같은 정사각형을 컴퍼스와 자로 작도하는 문제를 일컫는다. 이는 <a href="/wiki/%EC%9B%90%EC%A3%BC%EC%9C%A8" title="원주율">원주율</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span>가 <a href="/wiki/%EC%B4%88%EC%9B%94%EC%88%98" title="초월수">초월수</a>이므로 불가능하다. </p> <div class="mw-heading mw-heading2"><h2 id="기타_관련_주제"><span id=".EA.B8.B0.ED.83.80_.EA.B4.80.EB.A0.A8_.EC.A3.BC.EC.A0.9C"></span>기타 관련 주제</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=22" title="부분 편집: 기타 관련 주제"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="내접원,_외접원,_방접원"><span id=".EB.82.B4.EC.A0.91.EC.9B.90.2C_.EC.99.B8.EC.A0.91.EC.9B.90.2C_.EB.B0.A9.EC.A0.91.EC.9B.90"></span>내접원, 외접원, 방접원</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=23" title="부분 편집: 내접원, 외접원, 방접원"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>모든 삼각형은 유일한 <a href="/wiki/%EB%82%B4%EC%A0%91%EC%9B%90" title="내접원">내접원</a> 및 <a href="/wiki/%EC%99%B8%EC%A0%91%EC%9B%90" title="외접원">외접원</a>과 정확히 3개의 <a href="/wiki/%EB%B0%A9%EC%A0%91%EC%9B%90" title="방접원">방접원</a>을 갖는다. 그러나, 일반적으로 <a href="/wiki/%EB%8B%A4%EA%B0%81%ED%98%95" title="다각형">다각형</a>은 내접원이나 외접원을 가질 필요가 없다. 어떤 다각형이 모든 변에 접하는 원을 가질 경우, 이 다각형을 <a href="/w/index.php?title=%EC%99%B8%EC%A0%91_%EB%8B%A4%EA%B0%81%ED%98%95&action=edit&redlink=1" class="new" title="외접 다각형 (없는 문서)">외접 다각형</a>이라고 한다. 어떤 다각형이 모든 꼭짓점을 지나는 원을 가질 경우, 이 다각형을 <a href="/wiki/%EB%82%B4%EC%A0%91_%EB%8B%A4%EA%B0%81%ED%98%95" class="mw-redirect" title="내접 다각형">내접 다각형</a>이라고 한다. 동시에 외접 다각형이며 내접 다각형인 다각형을 <a href="/w/index.php?title=%EC%9D%B4%EC%A4%91%EC%A4%91%EC%8B%AC_%EB%8B%A4%EA%B0%81%ED%98%95&action=edit&redlink=1" class="new" title="이중중심 다각형 (없는 문서)">이중중심 다각형</a>이라고 한다. 예를 들어, 모든 삼각형과 모든 <a href="/wiki/%EC%A0%95%EB%8B%A4%EA%B0%81%ED%98%95" title="정다각형">정다각형</a>은 이중중심 다각형이다. </p><p>주어진 원의 내접 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>각형 가운데 넓이가 가장 큰 것은 정<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>각형이다.<sup id="cite_ref-Isaacs_4-14" class="reference"><a href="#cite_note-Isaacs-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><span class="reference" style="white-space: nowrap;"><sup>:35, §1G</sup></span> </p> <div class="mw-heading mw-heading2"><h2 id="문학"><span id=".EB.AC.B8.ED.95.99"></span>문학</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=24" title="부분 편집: 문학"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>에드윈 A. 애보트의 공상 <a href="/wiki/%EC%88%98%ED%95%99" title="수학">수학</a> 소설 《<a href="/wiki/%ED%94%8C%EB%9E%AB%EB%9E%9C%EB%93%9C" title="플랫랜드">플랫랜드</a>》에서는 원이 <a href="/wiki/%EC%84%B1%EC%A7%81%EC%9E%90" title="성직자">성직자</a>로 출현하며, 평면도형들 중 가장 고귀한 계급으로 여겨진다.</li></ul> <div class="mw-heading mw-heading2"><h2 id="같이_보기"><span id=".EA.B0.99.EC.9D.B4_.EB.B3.B4.EA.B8.B0"></span>같이 보기</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=25" title="부분 편집: 같이 보기"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%EC%9D%BC%EA%B0%81%ED%98%95" title="일각형">일각형</a></li> <li><a href="/wiki/%EA%B5%AC_(%EA%B8%B0%ED%95%98%ED%95%99)" title="구 (기하학)">구</a></li> <li><a href="/wiki/%EC%9B%90%EA%B8%B0%EB%91%A5" title="원기둥">원기둥</a></li> <li><a href="/wiki/%EB%B6%80%EC%B1%84%EA%BC%B4" title="부채꼴">부채꼴</a></li> <li><a href="/wiki/%EC%BB%B4%ED%8D%BC%EC%8A%A4" title="컴퍼스">컴퍼스</a></li> <li><a href="/wiki/%EC%9B%90%EC%A3%BC%EC%9C%A8" title="원주율">원주율</a></li> <li><a href="/wiki/%ED%95%98%EC%9C%84%ED%97%8C%EC%8A%A4_%EC%9B%90%EB%A6%AC" title="하위헌스 원리">하위헌스 원리</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="각주"><span id=".EA.B0.81.EC.A3.BC"></span>각주</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%9B%90_(%EA%B8%B0%ED%95%98%ED%95%99)&action=edit&section=26" title="부분 편집: 각주"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r35556958">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-Gibson-1"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Gibson_1-0">가</a></sup> <sup><a href="#cite_ref-Gibson_1-1">나</a></sup> <sup><a href="#cite_ref-Gibson_1-2">다</a></sup> <sup><a href="#cite_ref-Gibson_1-3">라</a></sup></span> <span class="reference-text"><cite class="citation book">Gibson, C. G. (2003). 《Elementary Euclidean geometry》 (영어). Cambridge: Cambridge University Press. <a href="/wiki/%EA%B5%AD%EC%A0%9C_%ED%91%9C%EC%A4%80_%EB%8F%84%EC%84%9C_%EB%B2%88%ED%98%B8" class="mw-redirect" title="국제 표준 도서 번호">ISBN</a> <a href="/wiki/%ED%8A%B9%EC%88%98:%EC%B1%85%EC%B0%BE%EA%B8%B0/978-0-521-83448-3" title="특수:책찾기/978-0-521-83448-3"><bdi>978-0-521-83448-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Elementary+Euclidean+geometry&rft.place=Cambridge&rft.pub=Cambridge+University+Press&rft.date=2003&rft.isbn=978-0-521-83448-3&rft.aulast=Gibson&rft.aufirst=C.+G.&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EC%9B%90+%28%EA%B8%B0%ED%95%98%ED%95%99%29" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Martin-2"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Martin_2-0">가</a></sup> <sup><a href="#cite_ref-Martin_2-1">나</a></sup> <sup><a href="#cite_ref-Martin_2-2">다</a></sup> <sup><a href="#cite_ref-Martin_2-3">라</a></sup> <sup><a href="#cite_ref-Martin_2-4">마</a></sup> <sup><a href="#cite_ref-Martin_2-5">바</a></sup></span> <span class="reference-text"><cite class="citation book">Martin, George E. (1975). 《The Foundations of Geometry and the Non-Euclidean Plane》. Undergraduate Texts in Mathematics (영어). New York, NY: Springer. <a href="/wiki/%EB%94%94%EC%A7%80%ED%84%B8_%EA%B0%9D%EC%B2%B4_%EC%8B%9D%EB%B3%84%EC%9E%90" title="디지털 객체 식별자">doi</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1007%2F978-1-4612-5725-7">10.1007/978-1-4612-5725-7</a>. <a href="/wiki/%EA%B5%AD%EC%A0%9C_%ED%91%9C%EC%A4%80_%EB%8F%84%EC%84%9C_%EB%B2%88%ED%98%B8" class="mw-redirect" title="국제 표준 도서 번호">ISBN</a> <a href="/wiki/%ED%8A%B9%EC%88%98:%EC%B1%85%EC%B0%BE%EA%B8%B0/978-1-4612-5727-1" title="특수:책찾기/978-1-4612-5727-1"><bdi>978-1-4612-5727-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Foundations+of+Geometry+and+the+Non-Euclidean+Plane&rft.place=New+York%2C+NY&rft.series=Undergraduate+Texts+in+Mathematics&rft.pub=Springer&rft.date=1975&rft_id=info%3Adoi%2F10.1007%2F978-1-4612-5725-7&rft.isbn=978-1-4612-5727-1&rft.aulast=Martin&rft.aufirst=George+E.&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EC%9B%90+%28%EA%B8%B0%ED%95%98%ED%95%99%29" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Johnson-3"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Johnson_3-0">가</a></sup> <sup><a href="#cite_ref-Johnson_3-1">나</a></sup> <sup><a href="#cite_ref-Johnson_3-2">다</a></sup> <sup><a href="#cite_ref-Johnson_3-3">라</a></sup> <sup><a href="#cite_ref-Johnson_3-4">마</a></sup> <sup><a href="#cite_ref-Johnson_3-5">바</a></sup></span> <span class="reference-text"><cite class="citation book">Johnson, Roger A. (1960) [1929]. 《Advanced Euclidean Geometry》 (영어). New York, N. Y.: Dover Publications.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Advanced+Euclidean+Geometry&rft.place=New+York%2C+N.+Y.&rft.pub=Dover+Publications&rft.date=1960&rft.aulast=Johnson&rft.aufirst=Roger+A.&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EC%9B%90+%28%EA%B8%B0%ED%95%98%ED%95%99%29" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Isaacs-4"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Isaacs_4-0">가</a></sup> <sup><a href="#cite_ref-Isaacs_4-1">나</a></sup> <sup><a href="#cite_ref-Isaacs_4-2">다</a></sup> <sup><a href="#cite_ref-Isaacs_4-3">라</a></sup> <sup><a href="#cite_ref-Isaacs_4-4">마</a></sup> <sup><a href="#cite_ref-Isaacs_4-5">바</a></sup> <sup><a href="#cite_ref-Isaacs_4-6">사</a></sup> <sup><a href="#cite_ref-Isaacs_4-7">아</a></sup> <sup><a href="#cite_ref-Isaacs_4-8">자</a></sup> <sup><a href="#cite_ref-Isaacs_4-9">차</a></sup> <sup><a href="#cite_ref-Isaacs_4-10">카</a></sup> <sup><a href="#cite_ref-Isaacs_4-11">타</a></sup> <sup><a href="#cite_ref-Isaacs_4-12">파</a></sup> <sup><a href="#cite_ref-Isaacs_4-13">하</a></sup> <sup><a href="#cite_ref-Isaacs_4-14">거</a></sup></span> <span class="reference-text"><cite class="citation book">Isaacs, I. Martin (2001). 《Geometry for College Students》. The Brooks/Cole Series in Advanced Mathematics (영어). 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