{"id":156506,"date":"2022-03-26T01:49:57","date_gmt":"2022-03-25T20:19:57","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/radius-of-a-circle-definition-theorems-and-length-of-chord-of-circle-formula\/"},"modified":"2024-05-06T14:50:33","modified_gmt":"2024-05-06T09:20:33","slug":"radius-of-a-circle-definition-theorems-and-length-of-chord-of-circle-formula","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/","title":{"rendered":"Radius of a Circle"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/#Radius_of_a_Circle_Definition\" title=\"Radius of a Circle Definition\">Radius of a Circle Definition<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/#Definition_of_the_Radius_of_a_Circle_and_the_Chord\" title=\"Definition of the Radius of a Circle and the Chord\">Definition of the Radius of a Circle and the Chord<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/#Length_of_Chord_of_Circle_Formula\" title=\"Length of Chord of Circle Formula\">Length of Chord of Circle Formula<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/#What_is_a_Circle\" title=\"What is a Circle?\">What is a Circle?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/#Define_Radius_of_a_Circle\" title=\"Define Radius of a Circle\">Define Radius of a Circle<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/#Define_Relation_Between_Radius_of_a_Circle_and_Chord\" title=\"Define Relation Between Radius of a Circle and Chord\">Define Relation Between Radius of a Circle and Chord<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/#Chord_of_a_Circle_Theorems\" title=\"Chord of a Circle Theorems\">Chord of a Circle Theorems<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/#Theorem_1\" title=\"Theorem 1:\">Theorem 1:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/#Theorem_2\" title=\"Theorem 2:\">Theorem 2:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/#Length_of_Chord_of_Circle_Formula-2\" title=\"Length of Chord of Circle Formula\">Length of Chord of Circle Formula<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/#What_is_an_Arc_and_Chord_of_a_Circle\" title=\"What is an Arc and Chord of a Circle?\">What is an Arc and Chord of a Circle?<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Radius_of_a_Circle_Definition\"><\/span>Radius of a Circle Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The radius of a circle is the distance from the center of the circle to any point on the circle.<\/p>\n<p>The Diameter of a Circle is the length of the line that starts from one point on a circle to another point and passes through the centre of the circle, and it is equal to twice the radius of the circle. It is denoted by \u2018d\u2019 or \u2018D\u2019.<\/p>\n<p>The radius of a circle is the distance from its centre to any point on its edge, and it is equal to half the diameter of the circle. It is denoted by \u2018r\u2019 or \u2018R\u2019.<\/p>\n<p>The circumference of a circle is the distance around the edge of the circle, and it is equal to 3.14 times the radius of the circle. It is denoted by \u2018C\u2019.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Definition_of_the_Radius_of_a_Circle_and_the_Chord\"><\/span>Definition of the Radius of a Circle and the Chord<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The radius of a circle is the distance from the center of the circle to its edge. The chord is a line segment that connects two points on a circle.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Length_of_Chord_of_Circle_Formula\"><\/span>Length of Chord of Circle Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The length of chord of a circle is the distance between two points on the circumference of the circle. This distance can be found using the following formula:<\/p>\n<ul>\n<li>Chord length = circumference \u00f7 (2 \u00d7 pi)<\/li>\n<li>where pi is a constant equal to 3.14159.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"What_is_a_Circle\"><\/span>What is a Circle?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A Circle is a plane figure with all points on it equidistant from a common point within it.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Define_Radius_of_a_Circle\"><\/span>Define Radius of a Circle<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A radius of a circle is the distance from the center of the circle to its edge.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Define_Relation_Between_Radius_of_a_Circle_and_Chord\"><\/span>Define Relation Between Radius of a Circle and Chord<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A chord is a line segment that connects two points on a circle. The radius is the length of the line segment from the center of the circle to the chord.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Chord_of_a_Circle_Theorems\"><\/span>Chord of a Circle Theorems<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are three theorems associated with chords of a circle.<\/p>\n<ul>\n<li>The first is the theorem of perpendicularity, which states that the perpendicular bisector of a chord intersects the chord at its midpoint.<\/li>\n<li>The second is the theorem of equality of angles, which states that the angles at the points of intersection of two chords are equal.<\/li>\n<li>The third is the theorem of subtraction, which states that the angle between a chord and the tangent at its point of intersection is equal to the angle between the chord and the radius.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Theorem_1\"><\/span>Theorem 1:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>If \\(p\\) is a prime number and \\(a\\) is a natural number, then \\(p\\) divides \\(a\\) if and only if \\(p\\) is a factor of \\(a\\).<\/p>\n<p>Proof:<\/p>\n<p>We will show that \\(p\\) divides \\(a\\) if and only if \\(p\\) is a factor of \\(a\\).<\/p>\n<p>If \\(p\\) divides \\(a\\), then \\(p\\) is a factor of \\(a\\).<\/p>\n<p>If \\(p\\) is a factor of \\(a\\), then \\(p\\) divides \\(a\\).<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Theorem_2\"><\/span>Theorem 2:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>If a and b are positive integers, then their product a\u00d7b is also a positive integer.<\/p>\n<p>Proof:<\/p>\n<p>We will use the well-ordering principle to show that a\u00d7b is a positive integer.<\/p>\n<p>Suppose a\u00d7b is not a positive integer. This means there exists a positive integer c such that a\u00d7b &lt; c. But then a\u00d7b \u2013 c is a negative integer, which is impossible. Therefore, a\u00d7b is a positive integer.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Length_of_Chord_of_Circle_Formula-2\"><\/span>Length of Chord of Circle Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The length of the chord of a circle is the length of the line segment that connects the points of the circle that are the endpoints of the chord. The length of a chord can be found using the following formula:<\/p>\n<p>The length of a chord is given by the following equation:<\/p>\n<p>where &#8220;r&#8221; is the radius of the circle and &#8220;d&#8221; is the distance between the endpoints of the chord.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_an_Arc_and_Chord_of_a_Circle\"><\/span>What is an Arc and Chord of a Circle?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>An arc is a portion of the circumference of a circle. A chord is a line segment that connects two points on a circle.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Radius of a Circle Definition The radius of a circle is the distance from the center of the circle to [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Radius of a Circle","_yoast_wpseo_title":"Radius of a Circle \u2013 Definition, Theorems, and Length of Chord of Circle Formula","_yoast_wpseo_metadesc":"The radius of a circle is the distance from the center of the circle to any point on the circle only at Infinitylearn.com.","custom_permalink":"maths\/radius-of-a-circle\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Radius of a Circle \u2013 Definition, Theorems, and Length of Chord of Circle Formula<\/title>\n<meta name=\"description\" content=\"The radius of a circle is the distance from the center of the circle to any point on the circle only at Infinitylearn.com.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Radius of a Circle \u2013 Definition, Theorems, and Length of Chord of Circle Formula\" \/>\n<meta property=\"og:description\" content=\"The radius of a circle is the distance from the center of the circle to any point on the circle only at Infinitylearn.com.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:published_time\" content=\"2022-03-25T20:19:57+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-05-06T09:20:33+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1008\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"vipin\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Radius of a Circle \u2013 Definition, Theorems, and Length of Chord of Circle Formula","description":"The radius of a circle is the distance from the center of the circle to any point on the circle only at Infinitylearn.com.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/","og_locale":"en_US","og_type":"article","og_title":"Radius of a Circle \u2013 Definition, Theorems, and Length of Chord of Circle Formula","og_description":"The radius of a circle is the distance from the center of the circle to any point on the circle only at Infinitylearn.com.","og_url":"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_published_time":"2022-03-25T20:19:57+00:00","article_modified_time":"2024-05-06T09:20:33+00:00","og_image":[{"width":1920,"height":1008,"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_creator":"@InfinityLearn_","twitter_site":"@InfinityLearn_","twitter_misc":{"Written by":"vipin","Est. reading time":"4 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/","name":"Radius of a Circle \u2013 Definition, Theorems, and Length of Chord of Circle Formula","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"datePublished":"2022-03-25T20:19:57+00:00","dateModified":"2024-05-06T09:20:33+00:00","description":"The radius of a circle is the distance from the center of the circle to any point on the circle only at Infinitylearn.com.","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"Radius of a Circle"}]},{"@type":"Article","@id":"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/#article","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/#webpage"},"author":{"@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/d931698bc4645b2739855720864f30e2"},"headline":"Radius of a Circle","datePublished":"2022-03-25T20:19:57+00:00","dateModified":"2024-05-06T09:20:33+00:00","mainEntityOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/radius-of-a-circle\/#webpage"},"wordCount":658,"publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"articleSection":["Maths"],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/d931698bc4645b2739855720864f30e2","name":"vipin","image":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/c9a84adf9d11e7ad01332089c3e52538?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/c9a84adf9d11e7ad01332089c3e52538?s=96&d=mm&r=g","caption":"vipin"},"sameAs":["http:\/\/surge.infinitylearn.com"],"url":"https:\/\/infinitylearn.com\/surge\/author\/vipin\/"}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/156506"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/comments?post=156506"}],"version-history":[{"count":0,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/156506\/revisions"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=156506"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=156506"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/tags?post=156506"},{"taxonomy":"table_tags","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/table_tags?post=156506"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}