{"id":22879,"date":"2023-06-10T07:26:00","date_gmt":"2023-06-10T01:56:00","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=22879"},"modified":"2026-01-23T20:25:47","modified_gmt":"2026-01-23T14:55:47","slug":"circle-properties-circle-formulas-circle-area-circle-circumference","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/circle-properties-circle-formulas-circle-area-circle-circumference\/","title":{"rendered":"Circle Formulas -What is a Circle and its properties? (Definition &#038; Examples)"},"content":{"rendered":"<span class=\"rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">A <\/span> <span class=\"rt-time\">8<\/span> <span class=\"rt-label rt-postfix\">min read <\/span><\/span>\n<p>A circle is a closed shape formed by tracing a point that moves in a plane such that its distance from a given point is constant. The word circle is derived from the Greek word <strong><em>kirkos<\/em><\/strong>, meaning hoop or ring. In this article, we cover the various circle formulas, properties of a circle &amp; important terms related to circles.<\/p>\n\n\n<div class=\"ub-buttons align-button-center\"  id=\"ub-button-d19aa9a3-9d42-4a57-84fe-67773f57c5b8\"><div class=\"ub-button-container\">\n    <a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" target=\"_blank\" rel=\"noopener noreferrer external\" class=\"ub-button-block-main ub-button-small ub-button-flex-small\" role=\"button\" data-wpel-link=\"external\">\n    <div class=\"ub-button-content-holder\"><span class=\"ub-button-icon-holder\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\"height=\"25\", width=\"25\"viewBox=\"0, 0, 448, 512\"><path fill=\"currentColor\" d=\"M246.6 233.4l-160-160c-12.5-12.5-32.75-12.5-45.25 0s-12.5 32.75 0 45.25L178.8 256l-137.4 137.4c-12.5 12.5-12.5 32.75 0 45.25C47.63 444.9 55.81 448 64 448s16.38-3.125 22.62-9.375l160-160C259.1 266.1 259.1 245.9 246.6 233.4zM438.6 233.4l-160-160c-12.5-12.5-32.75-12.5-45.25 0s-12.5 32.75 0 45.25L370.8 256l-137.4 137.4c-12.5 12.5-12.5 32.75 0 45.25C239.6 444.9 247.8 448 256 448s16.38-3.125 22.62-9.375l160-160C451.1 266.1 451.1 245.9 438.6 233.4z\"><\/svg><\/span><span class=\"ub-button-block-btn\"><strong>Start Free GMAT Preparation<\/strong><\/span>\n    <\/div><\/a><\/div><\/div>\n\n\n<figure class=\"wp-block-image aligncenter\"><a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\"><img loading=\"lazy\" width=\"1024\" height=\"576\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Circle-Formula-1024x576.jpg\" alt=\"Properties of Circle &amp; Circle Formulas\" class=\"wp-image-22945\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Circle-Formula-1024x576.jpg 1024w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Circle-Formula-300x169.jpg 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Circle-Formula-768x432.jpg 768w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Circle-Formula-1080x608.jpg 1080w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Circle-Formula.jpg 1920w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/a><\/figure>\n\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-4aad4c96-3dd0-4268-98c5-f31824e141ea\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-header-container\"><div class=\"ub_table-of-contents-header\">\n                    <div class=\"ub_table-of-contents-title\">Following is a brief outline of the topics that we will cover in this article:<\/div><\/div><\/div><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=\"https:\/\/e-gmat.com\/blogs\/circle-properties-circle-formulas-circle-area-circle-circumference\/#0-definition-of-a-circle-\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Definition of a Circle<\/a><\/li><li><a href=\"https:\/\/e-gmat.com\/blogs\/circle-properties-circle-formulas-circle-area-circle-circumference\/#1-terms-related-to-circles-amp-circle-formulas\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Terms related to Circles &amp; Circle formulas<\/a><ul><li><a href=\"https:\/\/e-gmat.com\/blogs\/circle-properties-circle-formulas-circle-area-circle-circumference\/#2-center\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Center<\/a><\/li><li><a href=\"https:\/\/e-gmat.com\/blogs\/circle-properties-circle-formulas-circle-area-circle-circumference\/#3-radius\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Radius<\/a><\/li><li><a href=\"https:\/\/e-gmat.com\/blogs\/circle-properties-circle-formulas-circle-area-circle-circumference\/#4-diameter\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Diameter<\/a><\/li><li><a href=\"https:\/\/e-gmat.com\/blogs\/circle-properties-circle-formulas-circle-area-circle-circumference\/#5-circumference\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Circumference<\/a><\/li><li><a href=\"https:\/\/e-gmat.com\/blogs\/circle-properties-circle-formulas-circle-area-circle-circumference\/#6-arc-of-a-circle\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Arc of a circle<\/a><\/li><li><a href=\"https:\/\/e-gmat.com\/blogs\/circle-properties-circle-formulas-circle-area-circle-circumference\/#7-sector-of-a-circle\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Sector of a circle:<\/a><\/li><li><a href=\"https:\/\/e-gmat.com\/blogs\/circle-properties-circle-formulas-circle-area-circle-circumference\/#8-semi-circle\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Semi-circle<\/a><\/li><\/ul><\/li><li><a href=\"https:\/\/e-gmat.com\/blogs\/circle-properties-circle-formulas-circle-area-circle-circumference\/#9-important-properties-of-circles-related-to-lines\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Important Properties of Circles &#8211; Related to Lines<\/a><ul><li><a href=\"https:\/\/e-gmat.com\/blogs\/circle-properties-circle-formulas-circle-area-circle-circumference\/#11-chord\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Chord<\/a><\/li><li><a href=\"https:\/\/e-gmat.com\/blogs\/circle-properties-circle-formulas-circle-area-circle-circumference\/#13-tangent\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Tangent<\/a><\/li><\/ul><\/li><li><a href=\"https:\/\/e-gmat.com\/blogs\/circle-properties-circle-formulas-circle-area-circle-circumference\/#15-important-properties-of-circles-related-to-angles\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Important Properties of Circles &#8211; Related to Angles<\/a><ul><li><a href=\"https:\/\/e-gmat.com\/blogs\/circle-properties-circle-formulas-circle-area-circle-circumference\/#17-inscribed-angle\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Inscribed Angle<\/a><\/li><li><a href=\"https:\/\/e-gmat.com\/blogs\/circle-properties-circle-formulas-circle-area-circle-circumference\/#19-property-of-central-angles\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Central Angle<\/a><\/li><\/ul><\/li><li><a href=\"https:\/\/e-gmat.com\/blogs\/circle-properties-circle-formulas-circle-area-circle-circumference\/#20-important-circle-formulas-area-and-perimeter-\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Important Circle Formulas:<\/a><ul><li><a href=\"https:\/\/e-gmat.com\/blogs\/circle-properties-circle-formulas-circle-area-circle-circumference\/#21-perimeter\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Perimeter:<\/a><\/li><li><a href=\"https:\/\/e-gmat.com\/blogs\/circle-properties-circle-formulas-circle-area-circle-circumference\/#22-area\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Area:<\/a><\/li><\/ul><\/li><li><a href=\"https:\/\/e-gmat.com\/blogs\/circle-properties-circle-formulas-circle-area-circle-circumference\/#24-application-of-the-circle-properties-amp-circle-formulas-in-the-questions\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Application of the properties in the GMAT questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-b0434f1c-8eb5-4628-8b33-4739fcd9ed3e\">\n\n\n<p>Geometry is an essential topic to ace if you plan to <a href=\"https:\/\/e-gmat.com\/blogs\/how-to-score-700-on-gmat-7-steps\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">score 700+ on the GMAT<\/a>. Let us help you achieve mastery in GMAT Geometry. Start by <a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\">signing up for a free trial<\/a>, get access to 400+ practice questions, and learn from the best in the industry. After all, we are the<a href=\"https:\/\/gmatclub.com\/reviews\/e-gmat-6\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\"> most reviewed company on GMATClub.<\/a><\/p>\n\n\n\n<p><br><em><strong><a href=\"https:\/\/e-gmat.com\/blogs\/gmat-q50-in-3-weeks-gmat-750-with-work-study-plan\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Richa<\/a>, <a href=\"https:\/\/e-gmat.com\/blogs\/gmat-710-wharton-first-time-test-takers-story\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Guillermo<\/a>, <a href=\"https:\/\/e-gmat.com\/blogs\/from-gmat-690-to-750-sireeshs-6-year-journey-to-ace-the-gmat\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Sireesh<\/a>, and <a href=\"https:\/\/e-gmat.com\/blogs\/how-raghav-scored-a-gmat-760-q50-v41-third-attempt\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Raghav<\/a> are just a few of the students that have achieved a Q50+ score in the GMAT Quant section using e-GMAT.<\/strong><\/em> <em>If you too wish to score Q50+ on the GMAT, here&#8217;s how we can help!<\/em><\/p>\n\n\n<\/div>\n\n\n<h2 id=\"0-definition-of-a-circle-\">Definition of a Circle <\/h2>\n\n\n\n<p>When a <em><u>set of all points<\/u><\/em> that are <em><u>at a fixed distance from a fixed point<\/u><\/em> are joined then the geometrical figure obtained is called circle.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/circle-definition.png\" alt=\"definition of a circle\" class=\"wp-image-22883\"\/><\/figure>\n\n\n\n<p>Let us now learn a bit about the terminology used in circles.<\/p>\n\n\n\n<h2 id=\"1-terms-related-to-circles-amp-circle-formulas\">Terms related to Circles &amp; Circle formulas<\/h2>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"1024\" height=\"574\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Terms-Related-to-Circles-1024x574.png\" alt=\"Properties of Circle - Terms Related to Circles\" class=\"wp-image-22937\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Terms-Related-to-Circles-1024x574.png 1024w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Terms-Related-to-Circles-300x168.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Terms-Related-to-Circles-768x430.png 768w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Terms-Related-to-Circles-1080x605.png 1080w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<blockquote class=\"wp-block-quote\"><p><strong>Take a <a href=\"https:\/\/resources.e-gmat.com\/take-sigma-x-mock\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\">free GMAT mock<\/a> to understand your baseline score and start your GMAT prep with our <a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\">free trial<\/a>. We are the&nbsp;<a href=\"https:\/\/gmatclub.com\/reviews\/e-gmat-6\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\">most reviewed online GMAT Prep company<\/a>&nbsp;with 2500+ reviews on GMATClub<\/strong>.<\/p><\/blockquote>\n\n\n<div class=\"ub-buttons align-button-center\"  id=\"ub-button-28e3a911-8bc2-4abc-9395-9c8fdd07c5a9\"><div class=\"ub-button-container\">\n    <a href=\"https:\/\/resources.e-gmat.com\/take-sigma-x-mock\" target=\"_blank\" rel=\"noopener noreferrer external\" class=\"ub-button-block-main ub-button-medium\" role=\"button\" data-wpel-link=\"external\">\n    <div class=\"ub-button-content-holder\"><span class=\"ub-button-icon-holder\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\"height=\"30\", width=\"30\"viewBox=\"0, 0, 448, 512\"><path fill=\"currentColor\" d=\"M246.6 233.4l-160-160c-12.5-12.5-32.75-12.5-45.25 0s-12.5 32.75 0 45.25L178.8 256l-137.4 137.4c-12.5 12.5-12.5 32.75 0 45.25C47.63 444.9 55.81 448 64 448s16.38-3.125 22.62-9.375l160-160C259.1 266.1 259.1 245.9 246.6 233.4zM438.6 233.4l-160-160c-12.5-12.5-32.75-12.5-45.25 0s-12.5 32.75 0 45.25L370.8 256l-137.4 137.4c-12.5 12.5-12.5 32.75 0 45.25C239.6 444.9 247.8 448 256 448s16.38-3.125 22.62-9.375l160-160C451.1 266.1 451.1 245.9 438.6 233.4z\"><\/svg><\/span><span class=\"ub-button-block-btn\">Take a free mock<\/span>\n    <\/div><\/a><\/div><\/div>\n\n\n<h3 id=\"2-center\">Center<\/h3>\n\n\n\n<p>The fixed point in the circle is called the center.<\/p>\n\n\n\n<ul><li>So, the set of points are at a fixed distance from the center of the circle.<\/li><\/ul>\n\n\n\n<h3 id=\"3-radius\">Radius<\/h3>\n\n\n\n<p>Radius is the fixed distance between the center and the set of points. It is denoted by <em><u>\u201cR\u201d<\/u><\/em><u>.<\/u><\/p>\n\n\n\n<h3 id=\"4-diameter\">Diameter<\/h3>\n\n\n\n<p>The diameter is a line segment, having boundary points of circles as the endpoints and passing through the center.<\/p>\n\n\n\n<ul><li>So, logically a diameter can be broken into two parts:\n<ul>\n<li>One part from one boundary point of the circle to the center<\/li>\n<li>And, the other part from the center to another boundary point.\n<ul>\n<li>Hence, Diameter = Twice the length of the radius or <strong><u>\u201cD = 2R\u201d<\/u><\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<h3 id=\"5-circumference\">Circumference<\/h3>\n\n\n\n<p>It is the measure of the outside boundary of the circle.<\/p>\n\n\n\n<p>So, the <em><u>length of the circle or the perimeter of the circle<\/u><\/em> is called Circumference.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"384\" height=\"289\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/cicumference-of-a-circle.png\" alt=\"circumference of a circle\" class=\"wp-image-22882\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/cicumference-of-a-circle.png 384w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/cicumference-of-a-circle-300x226.png 300w\" sizes=\"(max-width: 384px) 100vw, 384px\" \/><\/figure>\n\n\n\n<h3 id=\"6-arc-of-a-circle\">Arc of a circle<\/h3>\n\n\n\n<p>The arc of a circle is a portion of the circumference.<\/p>\n\n\n\n<p>From any two points that lie on the boundary of the circle, two arcs can be created: A Minor and a Major Arc.<\/p>\n\n\n\n<ul><li><strong>Minor arc: <\/strong>The shorter arc created by two points.<\/li><li><strong>Major Arc:<\/strong> The longer arc created by two points.<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"341\" height=\"327\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/arc-of-a-circle.png\" alt=\"arc of a circle\" class=\"wp-image-22880\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/arc-of-a-circle.png 341w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/arc-of-a-circle-300x288.png 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><\/figure>\n\n\n\n<h3 id=\"7-sector-of-a-circle\">Sector of a circle:<\/h3>\n\n\n\n<p>A Sector is formed by joining the endpoints of an arc with the center.<\/p>\n\n\n\n<ul><li>On joining the endpoints with the center, two sectors will be obtained: Minor and Major.\n<ul>\n<li>By default, we only consider the Minor sector unless it is mentioned otherwise.<\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/sector-of-a-circle.png\" alt=\"sector of a circle\" class=\"wp-image-22893\"\/><\/figure>\n\n\n\n<h3 id=\"8-semi-circle\">Semi-circle<\/h3>\n\n\n\n<p>A semi-circle is half part of the circle <em>or,<\/em><\/p>\n\n\n\n<ul><li>A semi-circle is obtained when a circle is divided into two equal parts.<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"230\" height=\"164\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Semi-circle.png\" alt=\"semi circle\" class=\"wp-image-22894\"\/><\/figure>\n\n\n\n<p>Now that we know all the terminologies related to the circles, let us learn about the properties of a circle.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote\"><p><strong>Geometry is an essential topic to ace if you plan to <a href=\"https:\/\/e-gmat.com\/blogs\/how-to-score-700-on-gmat-7-steps\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">score 700+ on the GMAT<\/a>. Let us help you achieve mastery in GMAT Geometry. Start by <a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\">signing up for a free trial<\/a> and learn from the best in the industry. After all, we are the most reviewed company on gmatclub.<\/strong><\/p><p><strong><em><a href=\"https:\/\/e-gmat.com\/blogs\/gmat-q50-in-3-weeks-gmat-750-with-work-study-plan\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Richa<\/a>, <a href=\"https:\/\/e-gmat.com\/blogs\/gmat-710-wharton-first-time-test-takers-story\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Guillermo<\/a>, <a href=\"https:\/\/e-gmat.com\/blogs\/from-gmat-690-to-750-sireeshs-6-year-journey-to-ace-the-gmat\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Sireesh<\/a>, and <a href=\"https:\/\/e-gmat.com\/blogs\/how-raghav-scored-a-gmat-760-q50-v41-third-attempt\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Raghav<\/a> are just a few of the students that have achieved a Q50+ score in the GMAT Quant section using e-GMAT.<\/em> <em>Get started with our free trial today if you too wish to score Q50+ on the GMAT!<\/em><\/strong><\/p><\/blockquote>\n\n\n<div class=\"ub-buttons align-button-center\"  id=\"ub-button-9ba332c1-b0f5-482d-a03b-1882b686faed\"><div class=\"ub-button-container\">\n    <a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" target=\"_blank\" rel=\"noopener noreferrer external\" class=\"ub-button-block-main ub-button-medium\" role=\"button\" data-wpel-link=\"external\">\n    <div class=\"ub-button-content-holder\"><span class=\"ub-button-icon-holder\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\"height=\"30\", width=\"30\"viewBox=\"0, 0, 512, 512\"><path fill=\"currentColor\" d=\"M256 0C114.6 0 0 114.6 0 256c0 141.4 114.6 256 256 256s256-114.6 256-256C512 114.6 397.4 0 256 0zM406.6 278.6l-103.1 103.1c-12.5 12.5-32.75 12.5-45.25 0s-12.5-32.75 0-45.25L306.8 288H128C110.3 288 96 273.7 96 256s14.31-32 32-32h178.8l-49.38-49.38c-12.5-12.5-12.5-32.75 0-45.25s32.75-12.5 45.25 0l103.1 103.1C414.6 241.3 416 251.1 416 256C416 260.9 414.6 270.7 406.6 278.6z\"><\/svg><\/span><span class=\"ub-button-block-btn\">Take a free trial<\/span>\n    <\/div><\/a><\/div><div class=\"ub-button-container\">\n    <a href=\"https:\/\/resources.e-gmat.com\/take-sigma-x-mock\" target=\"_blank\" rel=\"noopener noreferrer external\" class=\"ub-button-block-main ub-button-medium\" role=\"button\" data-wpel-link=\"external\">\n    <div class=\"ub-button-content-holder\"><span class=\"ub-button-icon-holder\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\"height=\"30\", width=\"30\"viewBox=\"0, 0, 448, 512\"><path fill=\"currentColor\" d=\"M246.6 233.4l-160-160c-12.5-12.5-32.75-12.5-45.25 0s-12.5 32.75 0 45.25L178.8 256l-137.4 137.4c-12.5 12.5-12.5 32.75 0 45.25C47.63 444.9 55.81 448 64 448s16.38-3.125 22.62-9.375l160-160C259.1 266.1 259.1 245.9 246.6 233.4zM438.6 233.4l-160-160c-12.5-12.5-32.75-12.5-45.25 0s-12.5 32.75 0 45.25L370.8 256l-137.4 137.4c-12.5 12.5-12.5 32.75 0 45.25C239.6 444.9 247.8 448 256 448s16.38-3.125 22.62-9.375l160-160C451.1 266.1 451.1 245.9 438.6 233.4z\"><\/svg><\/span><span class=\"ub-button-block-btn\">Take a free mock<\/span>\n    <\/div><\/a><\/div><\/div>\n\n\n<h2 id=\"9-important-properties-of-circles-related-to-lines\">Important Properties of Circles &#8211; Related to Lines<\/h2>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"1024\" height=\"608\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Lines-and-Circle-Formula-1024x608.png\" alt=\"Properties of Circle - Lines and Circle Formula\" class=\"wp-image-22936\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Lines-and-Circle-Formula-1024x608.png 1024w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Lines-and-Circle-Formula-300x178.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Lines-and-Circle-Formula-768x456.png 768w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Lines-and-Circle-Formula-1080x641.png 1080w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<h3 id=\"10-properties-related-to-lines-in-a-circle-properties-of-circle\">Properties related to Lines in a Circle | Properties of circle<\/h3>\n\n\n\n<h4 id=\"11-chord\">Chord<\/h4>\n\n\n\n<p>A chord is a line segment whose endpoints lie on the boundary of the circle.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"389\" height=\"235\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Chord-circle.png\" alt=\"chord in a circle\" class=\"wp-image-22881\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Chord-circle.png 389w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Chord-circle-300x181.png 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/figure>\n\n\n\n<h5 id=\"12-properties-of-chord\">Properties of Chord<\/h5>\n\n\n\n<ol><li>Perpendicular dropped from the center divides a chord into two equal parts.<\/li><\/ol>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"440\" height=\"308\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/properties-of-chord.png\" alt=\"properties of chord in a circle\" class=\"wp-image-22886\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/properties-of-chord.png 440w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/properties-of-chord-300x210.png 300w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><\/figure>\n\n\n\n<h4 id=\"13-tangent\">Tangent<\/h4>\n\n\n\n<p>Tangent is a line that <strong><em><u>touches<\/u><\/em><\/strong> the circle at any point.<\/p>\n\n\n\n<h5 id=\"14-properties-of-tangent\">Properties of Tangent<\/h5>\n\n\n\n<ol><li>Radius is always perpendicular to the tangent at the point where it touches the circle.<\/li><\/ol>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"428\" height=\"277\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/properties-of-tangent.png\" alt=\"properties of tangent\" class=\"wp-image-22890\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/properties-of-tangent.png 428w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/properties-of-tangent-300x194.png 300w\" sizes=\"(max-width: 428px) 100vw, 428px\" \/><\/figure>\n\n\n\n<h2 id=\"15-important-properties-of-circles-related-to-angles\">Important Properties of Circles &#8211; Related to Angles<\/h2>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"1024\" height=\"573\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Angles-inside-a-circle-1024x573.png\" alt=\"Properties of Circle - Angles inside a circle\" class=\"wp-image-22935\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Angles-inside-a-circle-1024x573.png 1024w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Angles-inside-a-circle-300x168.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Angles-inside-a-circle-768x430.png 768w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Angles-inside-a-circle-1080x604.png 1080w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<blockquote class=\"wp-block-quote\"><p><strong>Did you know a&nbsp;GMAT score of 730+ yields an incremental $500K in ROI? Start your GMAT Preparation by&nbsp;Signing up for our <a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\">FREE Trial&nbsp;<\/a>and get access to FREE online GMAT preparation resources. 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stroke-linecap=\"round\">\n              <path d=\"M22 11.08V12a10 10 0 1 1-5.93-9.14\"\/>\n              <path d=\"M22 4L12 14.01l-3-3\"\/>\n            <\/svg>\n          <\/div>\n          <div>\n            <p class=\"egmat-cta-bullet-title\">Know which section to prioritize<\/p>\n            <p class=\"egmat-cta-bullet-desc\">Quant, Verbal, or DI \u2014 see where to focus first<\/p>\n          <\/div>\n        <\/div>\n        \n        <!-- Bullet 3 -->\n        <div class=\"egmat-cta-bullet\">\n          <div class=\"egmat-cta-icon-box\">\n            <svg width=\"18\" height=\"18\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"#fb923c\" stroke-width=\"2.5\" stroke-linecap=\"round\">\n              <path d=\"M18 20V10M12 20V4M6 20v-6\"\/>\n            <\/svg>\n          <\/div>\n          <div>\n            <p class=\"egmat-cta-bullet-title\">Define your target percentiles<\/p>\n            <p class=\"egmat-cta-bullet-desc\">Clear metrics for each section to hit your goal<\/p>\n  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class=\"ub-button-content-holder\"><span class=\"ub-button-icon-holder\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\"height=\"30\", width=\"30\"viewBox=\"0, 0, 512, 512\"><path fill=\"currentColor\" d=\"M256 0C114.6 0 0 114.6 0 256c0 141.4 114.6 256 256 256s256-114.6 256-256C512 114.6 397.4 0 256 0zM406.6 278.6l-103.1 103.1c-12.5 12.5-32.75 12.5-45.25 0s-12.5-32.75 0-45.25L306.8 288H128C110.3 288 96 273.7 96 256s14.31-32 32-32h178.8l-49.38-49.38c-12.5-12.5-12.5-32.75 0-45.25s32.75-12.5 45.25 0l103.1 103.1C414.6 241.3 416 251.1 416 256C416 260.9 414.6 270.7 406.6 278.6z\"><\/svg><\/span><span class=\"ub-button-block-btn\">Get Free Prep Resources<\/span>\n    <\/div><\/a><\/div><div class=\"ub-button-container\">\n    <a href=\"https:\/\/resources.e-gmat.com\/take-sigma-x-mock\" target=\"_blank\" rel=\"noopener noreferrer external\" class=\"ub-button-block-main ub-button-medium\" role=\"button\" data-wpel-link=\"external\">\n    <div class=\"ub-button-content-holder\"><span class=\"ub-button-icon-holder\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\"height=\"30\", width=\"30\"viewBox=\"0, 0, 448, 512\"><path fill=\"currentColor\" d=\"M246.6 233.4l-160-160c-12.5-12.5-32.75-12.5-45.25 0s-12.5 32.75 0 45.25L178.8 256l-137.4 137.4c-12.5 12.5-12.5 32.75 0 45.25C47.63 444.9 55.81 448 64 448s16.38-3.125 22.62-9.375l160-160C259.1 266.1 259.1 245.9 246.6 233.4zM438.6 233.4l-160-160c-12.5-12.5-32.75-12.5-45.25 0s-12.5 32.75 0 45.25L370.8 256l-137.4 137.4c-12.5 12.5-12.5 32.75 0 45.25C239.6 444.9 247.8 448 256 448s16.38-3.125 22.62-9.375l160-160C451.1 266.1 451.1 245.9 438.6 233.4z\"><\/svg><\/span><span class=\"ub-button-block-btn\">Take a free mock<\/span>\n    <\/div><\/a><\/div><\/div>\n\n\n<h3 id=\"16-properties-related-to-angles-in-a-circle-properties-of-circle\">Properties related to Angles in a circle | Properties of Circle<\/h3>\n\n\n\n<h4 id=\"17-inscribed-angle\">Inscribed Angle<\/h4>\n\n\n\n<p>An inscribed angle is the angle formed between two chords when they meet on the boundary of the circle.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"345\" height=\"247\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Inscribed-angle-circle.png\" alt=\"angle inscribed in a circle\" class=\"wp-image-22884\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Inscribed-angle-circle.png 345w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Inscribed-angle-circle-300x215.png 300w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><\/figure>\n\n\n\n<h5 id=\"18-properties-of-inscribed-angles\">Properties of Inscribed Angles<\/h5>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"358\" height=\"271\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/properties-of-inscribed-angles-angle-subscribed-by-Arc.png\" alt=\"properties of inscribed angles angle subscribed by Arc\" class=\"wp-image-22888\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/properties-of-inscribed-angles-angle-subscribed-by-Arc.png 358w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/properties-of-inscribed-angles-angle-subscribed-by-Arc-300x227.png 300w\" sizes=\"(max-width: 358px) 100vw, 358px\" \/><\/figure>\n\n\n\n<p>1. Angles formed by the same arc on the circumference of the circle is always equal.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"330\" height=\"276\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/properties-of-inscribed-angles-angle-in-a-semicircle.png\" alt=\"properties of inscribed angles angle in a semicircle\" class=\"wp-image-22887\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/properties-of-inscribed-angles-angle-in-a-semicircle.png 330w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/properties-of-inscribed-angles-angle-in-a-semicircle-300x251.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><\/figure>\n\n\n\n<p>2. The angle in a <u>semi-circle<\/u> is always 90\u00b0.<span style=\"color: #333333; font-size: 18px;\">Central Angle<\/span><\/p>\n\n\n\n<p>A central angle is the angle formed when two-line segments meet such that one of the endpoints of both the line segment is at the center and another is at the boundary of the circle.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"291\" height=\"238\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/properties-of-inscribed-angles-central-angle.png\" alt=\"properties of inscribed angles central angle\" class=\"wp-image-22889\"\/><\/figure>\n\n\n\n<h4 id=\"19-property-of-central-angles\">&nbsp;Property of Central Angles<\/h4>\n\n\n\n<ul><li>An angle formed by an arc at the center is twice the <u>inscribed angle<\/u> formed by the same arc.<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"420\" height=\"270\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/properties-of-central-angle.png\" alt=\"pproperties of central angle in a circle\" class=\"wp-image-22885\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/properties-of-central-angle.png 420w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/properties-of-central-angle-300x193.png 300w\" sizes=\"(max-width: 420px) 100vw, 420px\" \/><\/figure>\n\n\n\n<h2 id=\"20-important-circle-formulas-area-and-perimeter-\">Important Circle Formulas: Area and Perimeter <\/h2>\n\n\n\n<p>The following are some mathematical formulae that will help you calculate the area and perimeter\/circumference of a circle.<\/p>\n\n\n\n<h3 id=\"21-perimeter\">Perimeter:<\/h3>\n\n\n\n<ul><li>Perimeter or the Circumference of the circle = 2 \u00d7 \u03c0 \u00d7 R.<\/li><li>Length of an Arc = (Central angle made by the arc\/360\u00b0) \u00d7 2 \u00d7 \u03c0 \u00d7 R.<\/li><\/ul>\n\n\n\n<h3 id=\"22-area\">Area:<\/h3>\n\n\n\n<ul><li>Area of the circle = \u03c0 \u00d7 R\u00b2<\/li><li>Area of the sector =(Central angle made by the sector\/360\u00b0) \u00d7 \u03c0 \u00d7 R\u00b2.<\/li><\/ul>\n\n\n\n<h2 id=\"23-summary-of-all-the-properties-of-a-circle\">Summary of all the Properties of a Circle<\/h2>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"790\" height=\"247\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/PROPERTIES-OF-A-CIRCLE.png\" alt=\"Properties of a circle\" class=\"wp-image-22896\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/PROPERTIES-OF-A-CIRCLE.png 790w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/PROPERTIES-OF-A-CIRCLE-300x94.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/PROPERTIES-OF-A-CIRCLE-768x240.png 768w\" sizes=\"(max-width: 790px) 100vw, 790px\" \/><\/figure>\n\n\n\n<p>Here is a summarized list of all the properties we have learned in the article up to this point.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Property<\/td><td>Element<\/td><td>Description<\/td><\/tr><tr><td>Lines in a circle<\/td><td>Chord<\/td><td>Perpendicular dropped from the center divides the chord into two equal parts.<\/td><\/tr><tr><td><\/td><td>Tangent<\/td><td>The radius is always perpendicular to the tangent at the point where it touches the circle.<\/td><\/tr><tr><td>Angles in a circle<\/td><td>Inscribed Angle<\/td><td>1. Angles formed by the same arc on the circumference of the circle is always equal.<br>2. The angle in a semi-circle is always 90.<\/td><\/tr><tr><td><\/td><td>Central Angle<\/td><td>The angle formed by an arc at the center is twice the inscribed angle formed by the same arc.<\/td><\/tr><tr><td>Important Formulae<\/td><td>Circumference of a circle<\/td><td>2 \u00d7 \u03c0 \u00d7 R.<\/td><\/tr><tr><td><\/td><td>Length of an arc<\/td><td>(Central angle made by the arc\/360\u00b0) \u00d7 2 \u00d7 \u03c0 \u00d7 R<\/td><\/tr><tr><td><\/td><td>Area of a circle<\/td><td>\u03c0 \u00d7 R\u00b2<\/td><\/tr><tr><td><\/td><td>Area of a sector<\/td><td>(Central angle made by the arc\/360\u00b0) \u00d7 \u03c0 \u00d7 R\u00b2<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<blockquote class=\"wp-block-quote\"><p><strong>Begin your GMAT preparation with the only prep company that has delivered more 700+ scores than any other GMAT club partner. Achieve GMAT 740+ with our AI driven tools that you personilzed feedback at every step of your GMAT journey. Take our <a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\">free trial<\/a> today!<\/strong><\/p><\/blockquote>\n\n\n<div class=\"ub-buttons align-button-center\"  id=\"ub-button-ce41bb7b-31e7-4d5b-bf68-98c272b279bd\"><div class=\"ub-button-container\">\n    <a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" target=\"_blank\" rel=\"noopener noreferrer external\" class=\"ub-button-block-main ub-button-medium ub-button-flex-medium\" role=\"button\" data-wpel-link=\"external\">\n    <div class=\"ub-button-content-holder\"><span class=\"ub-button-icon-holder\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\"height=\"30\", width=\"30\"viewBox=\"0, 0, 512, 512\"><path fill=\"currentColor\" d=\"M256 0C114.6 0 0 114.6 0 256c0 141.4 114.6 256 256 256s256-114.6 256-256C512 114.6 397.4 0 256 0zM406.6 278.6l-103.1 103.1c-12.5 12.5-32.75 12.5-45.25 0s-12.5-32.75 0-45.25L306.8 288H128C110.3 288 96 273.7 96 256s14.31-32 32-32h178.8l-49.38-49.38c-12.5-12.5-12.5-32.75 0-45.25s32.75-12.5 45.25 0l103.1 103.1C414.6 241.3 416 251.1 416 256C416 260.9 414.6 270.7 406.6 278.6z\"><\/svg><\/span><span class=\"ub-button-block-btn\">Get free prep resources<\/span>\n    <\/div><\/a><\/div><div class=\"ub-button-container\">\n    <a href=\"https:\/\/resources.e-gmat.com\/take-sigma-x-mock\" target=\"_blank\" rel=\"noopener noreferrer external\" class=\"ub-button-block-main ub-button-medium\" role=\"button\" data-wpel-link=\"external\">\n    <div class=\"ub-button-content-holder\"><span class=\"ub-button-icon-holder\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\"height=\"30\", width=\"30\"viewBox=\"0, 0, 448, 512\"><path fill=\"currentColor\" d=\"M246.6 233.4l-160-160c-12.5-12.5-32.75-12.5-45.25 0s-12.5 32.75 0 45.25L178.8 256l-137.4 137.4c-12.5 12.5-12.5 32.75 0 45.25C47.63 444.9 55.81 448 64 448s16.38-3.125 22.62-9.375l160-160C259.1 266.1 259.1 245.9 246.6 233.4zM438.6 233.4l-160-160c-12.5-12.5-32.75-12.5-45.25 0s-12.5 32.75 0 45.25L370.8 256l-137.4 137.4c-12.5 12.5-12.5 32.75 0 45.25C239.6 444.9 247.8 448 256 448s16.38-3.125 22.62-9.375l160-160C451.1 266.1 451.1 245.9 438.6 233.4z\"><\/svg><\/span><span class=\"ub-button-block-btn\">Take a free mock<\/span>\n    <\/div><\/a><\/div><\/div>\n\n\n<h2 id=\"24-application-of-the-circle-properties-amp-circle-formulas-in-the-questions\">Application of the circle properties &amp; circle formulas in the questions<\/h2>\n\n\n\n<h3 id=\"25-question-1\">Question 1<\/h3>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-de5da45a-9092-48ae-936a-57b2c4ec2a97\">\n\n\n<p>The lengths of two sides in a right-angle triangle other than hypotenuse are 6 cm and 8 cm. If this right-angle triangle is inscribed in a circle, then what is the area of the circle?<\/p>\n\n\n\n<ol><li>5 \u03c0<\/li><li>10 \u03c0<\/li><li>15 \u03c0<\/li><li>20 \u03c0<\/li><li>25 \u03c0<\/li><\/ol>\n\n\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 id=\"26-solution\">Solution<\/h4>\n\n\n\n<p><strong>Step 1: Given<\/strong><\/p>\n\n\n\n<ul><li>The lengths of two sides other than hypotenuse of a right triangle are 6 cm and 8 cm.<\/li><li>This triangle is inscribed in a circle.<\/li><\/ul>\n\n\n\n<p><strong>Step 2: To find<\/strong><\/p>\n\n\n\n<ul><li>Area of the circle.<\/li><\/ul>\n\n\n\n<p><strong>Step 3: Approach and Working out<\/strong><\/p>\n\n\n\n<p>Let us draw the diagrammatic representation.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"300\" height=\"302\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Question-1-circles.png\" alt=\"Question 1 circles\" class=\"wp-image-22891\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Question-1-circles.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Question-1-circles-150x150.png 150w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Question-1-circles-298x300.png 298w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/figure>\n\n\n\n<p>By applying the property that the angle in a semi-circle is 90\u00ba, we can say that AB is the diameter of the circle.<\/p>\n\n\n\n<ul><li>And, once we find the length of the diameter, we can find the radius, and then we can find the area of the circle as well.<\/li><\/ul>\n\n\n\n<p>Applying Pythagoras theorem in \u25b3 ABC,<\/p>\n\n\n\n<ul><li>AB\u00b2&nbsp;= AC\u00b2&nbsp;+ BC\u00b2\n<ul>\n<li>AB\u00b2&nbsp;= 6\u00b2&nbsp;+ 8\u00b2<sup>&nbsp;<\/sup>= 36 +64 = 100<\/li>\n<li>AB = 10 cm<\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<p>Since AB is the diameter, AB = 2R = 10<\/p>\n\n\n\n<ul><li>Hence, R = 5 cm.<\/li><\/ul>\n\n\n\n<p>Area of the circle = \u03c0 \u00d7 R\u00b2= \u03c0 \u00d7 5\u00b2&nbsp;= 25 \u03c0.<\/p>\n\n\n\n<p>Hence, the correct answer is option E.<\/p>\n\n\n\n<h3 id=\"27-question-2\">Question 2<\/h3>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-ed36d539-5a91-4a16-997b-eefa226b95b9\">\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"268\" height=\"243\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Question-2-circles.png\" alt=\"Question 2 circles\" class=\"wp-image-22892\"\/><\/figure>\n\n\n\n<p>In the diagram given above, O is the center of the circle. If OB = 5 cm and \u2220ABC = 30<sup>0<\/sup> then what the length of the arc AC?<\/p>\n\n\n\n<ol><li>5\u03c0\/6<\/li><li>5\u03c0\/3<\/li><li>5\u03c0\/2<\/li><li>5\u03c0<\/li><li>10\u03c0<\/li><\/ol>\n\n\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 id=\"28-solution\">Solution<\/h4>\n\n\n\n<p><strong>Step 1: Given<\/strong><\/p>\n\n\n\n<ul><li>OB = 5 cm<\/li><li>\u2220ABC = 30\u00b0<\/li><\/ul>\n\n\n\n<p><strong>Step 2: To find<\/strong><\/p>\n\n\n\n<ul><li>Length of the arc<\/li><\/ul>\n\n\n\n<p><strong>Step 3: Approach and Working out<\/strong><\/p>\n\n\n\n<ul><li>Length of the arc =&nbsp; (Central angle made by the arc\/360\u00b0) \u00d7 2 \u00d7 \u03c0 \u00d7 R.<\/li><\/ul>\n\n\n\n<p>To find the length of the arc, we need the value of two variable, the center angle made by the arc and the radius.<\/p>\n\n\n\n<ul><li>We are already given radius as OB = 5cm<\/li><li>We need to find the \u2220AOC<\/li><\/ul>\n\n\n\n<p>On visualizing the diagram, the inscribed angle by the arc AC is \u2220ABC, and the center angle by arc AC is \u2220AOC.<\/p>\n\n\n\n<ul><li>Hence, we can apply the property that the angle made at the center by an arc is twice the inscribed angle formed by the same arc.<\/li><li>Thus, \u2220AOC = 2 \u00d7 \u2220ABC = 2 \u00d7 30\u00b0<sup>&nbsp;<\/sup>= 60\u00b0<\/li><\/ul>\n\n\n\n<p>Now, we know the central angle formed by the arc as well.<\/p>\n\n\n\n<ul><li>Hence, length of the arc AC =(Central angle made by the arc\/360\u00b0) \u00d7 2 \u00d7 \u03c0 \u00d7 R.\n<ul>\n<li>=(60\u00b0\/360\u00b0) \u00d7 2 \u00d7 \u03c0 \u00d7 5.<\/li>\n<li>=(1\/6) \u00d7 2 \u00d7 \u03c0 \u00d7 5.<\/li>\n<li>=(5\u03c0\/3) cm<\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<p>Thus, the correct answer is option B.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote\"><p><strong>For more practice questions on triangles and geometry, sign up for our free trial. We have more than 400+ practice questions and 10+ hours of AI-driven video lessons.<\/strong> <strong>We are the&nbsp;most reviewed online GMAT Prep company&nbsp;with <a href=\"https:\/\/gmatclub.com\/reviews\/e-gmat-6\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\">2500+ reviews on GMATClub<\/a><\/strong><\/p><\/blockquote>\n\n\n<div class=\"ub-buttons align-button-center\"  id=\"ub-button-a803f260-4408-417a-8689-4ef9ba30bdc8\"><div class=\"ub-button-container\">\n    <a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" target=\"_blank\" rel=\"noopener noreferrer external\" class=\"ub-button-block-main ub-button-medium\" role=\"button\" data-wpel-link=\"external\">\n    <div class=\"ub-button-content-holder\"><span class=\"ub-button-icon-holder\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\"height=\"30\", width=\"30\"viewBox=\"0, 0, 512, 512\"><path fill=\"currentColor\" d=\"M256 0C114.6 0 0 114.6 0 256c0 141.4 114.6 256 256 256s256-114.6 256-256C512 114.6 397.4 0 256 0zM406.6 278.6l-103.1 103.1c-12.5 12.5-32.75 12.5-45.25 0s-12.5-32.75 0-45.25L306.8 288H128C110.3 288 96 273.7 96 256s14.31-32 32-32h178.8l-49.38-49.38c-12.5-12.5-12.5-32.75 0-45.25s32.75-12.5 45.25 0l103.1 103.1C414.6 241.3 416 251.1 416 256C416 260.9 414.6 270.7 406.6 278.6z\"><\/svg><\/span><span class=\"ub-button-block-btn\">Take a free trial<\/span>\n    <\/div><\/a><\/div><div class=\"ub-button-container\">\n    <a href=\"https:\/\/resources.e-gmat.com\/take-sigma-x-mock\" target=\"_blank\" rel=\"noopener noreferrer external\" class=\"ub-button-block-main ub-button-medium\" role=\"button\" data-wpel-link=\"external\">\n    <div class=\"ub-button-content-holder\"><span class=\"ub-button-icon-holder\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\"height=\"30\", width=\"30\"viewBox=\"0, 0, 448, 512\"><path fill=\"currentColor\" d=\"M246.6 233.4l-160-160c-12.5-12.5-32.75-12.5-45.25 0s-12.5 32.75 0 45.25L178.8 256l-137.4 137.4c-12.5 12.5-12.5 32.75 0 45.25C47.63 444.9 55.81 448 64 448s16.38-3.125 22.62-9.375l160-160C259.1 266.1 259.1 245.9 246.6 233.4zM438.6 233.4l-160-160c-12.5-12.5-32.75-12.5-45.25 0s-12.5 32.75 0 45.25L370.8 256l-137.4 137.4c-12.5 12.5-12.5 32.75 0 45.25C239.6 444.9 247.8 448 256 448s16.38-3.125 22.62-9.375l160-160C451.1 266.1 451.1 245.9 438.6 233.4z\"><\/svg><\/span><span class=\"ub-button-block-btn\">Take a free mock<\/span>\n    <\/div><\/a><\/div><\/div>\n\n\n<p>If you like this article here are a few more article related to geometry:<\/p>\n\n\n\n<ul><li><a href=\"https:\/\/e-gmat.com\/blogs\/gmat-geometry-formulas-concepts-on-triangles-part-1\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Triangle &#8211; Formulas and Concepts (Part-1)<\/a><\/li><li><a href=\"https:\/\/e-gmat.com\/blogs\/geometry-practice-questions-properties-of-triangles\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Triangle &#8211; Formulas and Concepts (Part-2)<\/a><\/li><li><a href=\"https:\/\/e-gmat.com\/blogs\/geometry-practice-problems-gmat-special-properties-of-triangles\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Triangle &#8211; Formulas and Concepts (Part-3)<\/a><\/li><li><a href=\"https:\/\/e-gmat.com\/blogs\/quadrilateral-properties-formulas-rectangle-square-parallelogram-rhombus-trapezium-trapezoid\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Quadrilaterals \u2013 Properties of rectangle, square, parallelogram, rhombus, trapezium<\/a><\/li><li><a href=\"https:\/\/e-gmat.com\/blogs\/gmat-geometry-questions-most-common-mistakes\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Most common mistakes in Geometry Questions &#8211; GMAT Quant<\/a><\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>A circle is a closed shape formed by tracing a point that moves in a plane such that its distance from a given point is constant. The word circle is derived from the Greek word kirkos, meaning hoop or ring. In this article, we cover the various circle formulas, properties of a circle &amp; important [&hellip;]<\/p>\n","protected":false},"author":102413,"featured_media":22945,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","ub_ctt_via":""},"categories":[104,94,60],"tags":[],"featured_image_src":"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/07\/Properties-of-Circle-Circle-Formula.jpg","author_info":{"display_name":"Ashutosh","author_link":"https:\/\/e-gmat.com\/blogs\/author\/ashutoshe-gmat-com\/"},"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.1.1 (Yoast SEO v17.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Circle Formulas -What is a Circle and its properties? 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