{"id":33652,"date":"2023-09-01T16:57:07","date_gmt":"2023-09-01T16:57:07","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=33652"},"modified":"2023-09-04T01:02:50","modified_gmt":"2023-09-04T01:02:50","slug":"circle-theorems-definition-formulas-steps-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/circle-theorems","title":{"rendered":"Circle Theorems: Definition, Formulas, Steps, Examples, FAQs"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-a65b0868-84c7-4d3d-a361-2cec5b55aa55\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><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:\/\/www.splashlearn.com\/math-vocabulary\/circle-theorems#0-what-are-circle-theorems-in-geometry>What Are Circle Theorems in Geometry?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/circle-theorems#1-important-terms-related-to-circle-theorems>Important Terms Related to Circle Theorems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/circle-theorems#12-circle-theorems-formulas>Circle Theorems Formulas<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/circle-theorems#15-solved-examples-on-circle-theorems>Solved Examples on Circle Theorems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/circle-theorems#16-practice-problems-on-circle-theorems>Practice Problems on Circle Theorems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/circle-theorems#17-frequently-asked-questions-on-circle-theorems>Frequently Asked Questions on Circle Theorems<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-are-circle-theorems-in-geometry\">What Are Circle Theorems in Geometry?<\/h2>\n\n\n\n<p><strong>The circle theorems in <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/geometry\"><strong>geometry<\/strong><\/a><strong> are statements that prove significant results about circles. These theorems provide important information or facts about various parts of a circle.<\/strong>&nbsp;<\/p>\n\n\n\n<p>We can use circle theorems and previous knowledge of properties of a circle to calculate missing angles. The circle angle theorems give us the rules for finding the measurements of angles in a circle.<\/p>\n\n\n\n<p>A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/circle\">circle<\/a> is a locus of points that are equidistant from a fixed point called center. Different theorems are based on the various parts of a circle, such as radius, central angles, tangents, sectors, the chords, etc. These theorems help us to solve many problems in geometry easily.<\/p>\n\n\n\n<p>Before we discuss the theorems, let\u2019s revise the parts of the circle using a diagram.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"344\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-parts.png\" alt=\"Parts of a circle\" class=\"wp-image-33660\" title=\"Parts of a circle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-parts.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-parts-300x166.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/count-upto-10-objects-in-circle\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/count_comp_hide_and_seek_10_gm.png\" alt=\"Count upto 10 Objects in Circle Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Count upto 10 Objects in Circle Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-circles-and-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_circles_rectangles_pt.png\" alt=\"Identify Circles and Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Circles and Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/match-rectangles-and-circles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_amusement_park_3_6_gm.png\" alt=\"Match Rectangles and Circles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Match Rectangles and Circles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            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});\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-important-terms-related-to-circle-theorems\">Important Terms Related to Circle Theorems<\/h2>\n\n\n\n<p>Here are a few important terms that are commonly used in the statements of circle theorems.<\/p>\n\n\n\n<p><strong>Subtended angle:<\/strong><strong> <\/strong>The angle made by something (arc, chord, etc) from a given viewpoint. An angle within a circle created by two chords meeting at a point on the circumference. In a circle, there are various angles that can be formed joining the endpoints of arcs and those angles are termed subtended angles.<\/p>\n\n\n\n<p><strong>Inscribed Angle:<\/strong> An angle made from points lying on the circle&#8217;s circumference. It can also be defined as the angle subtended at a point on the circle by two given points on the circle. Thus, it is formed by two chords that have a common endpoint on the circle.&nbsp;<\/p>\n\n\n\n<p><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/central-angle\"><strong>Central Angle<\/strong><\/a><strong>: <\/strong>An angle whose vertex is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"331\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/terms-in-circle-theorems.png\" alt=\"Important terms in circle theorems\" class=\"wp-image-33662\" title=\"Important terms in circle theorems\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/terms-in-circle-theorems.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/terms-in-circle-theorems-300x160.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/circle-equivalent-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/circle-equivalent-fractions.jpeg\" alt=\"Circle Equivalent Fractions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/squares-and-circles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/squares-and-circles.jpeg\" alt=\"Squares and Circles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-circle-theorems\">Circle Theorems<\/h2>\n\n\n\n<p>We will discuss the following circle theorems in detail.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Alternate segment theorem<\/li>\n\n\n\n<li>The angle at the center theorem<\/li>\n\n\n\n<li>Angles in the same segment theorem<\/li>\n\n\n\n<li>Angle in a semicircle theorem<\/li>\n\n\n\n<li>Chord of a circle theorem<\/li>\n\n\n\n<li>Cyclic quadrilateral theorem<\/li>\n\n\n\n<li>Tangent of a circle theorem-1<\/li>\n\n\n\n<li>Tangent of a circle theorem-2<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-circle-theorem-1-alternate-segment-theorem\">Circle Theorem 1: Alternate Segment Theorem<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-746ebee4-efbb-4b06-b813-7730211f3093\">\n\n\n<p><strong>Alternate Segment Theorem: <\/strong>For any circle, the angle formed between the tangent and the chord through the point of contact of the tangent is equal to the angle formed by the same chord in the alternate segment.<\/p>\n\n\n<\/div>\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"343\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/alternate-segment-theorem-diagram.png\" alt=\"Alternate segment theorem visual\" class=\"wp-image-33663\" title=\"Alternate segment theorem visual\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/alternate-segment-theorem-diagram.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/alternate-segment-theorem-diagram-300x166.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Here, according to the alternate segment theorem,&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2220x = \u2220BCE = \u2220BAC<\/li>\n<\/ul>\n\n\n\n<p>Here, \u2220BCE is the angle made by the tangent and the chord BC at the point of contact.<\/p>\n\n\n\n<p>\u2220BAC is the angle made by the same chord BC in the alternate segment BAC.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Similarly, \u2220y = \u2220ABC = \u2220ACD<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-circle-theorem-2-central-angle-theorem-the-angle-at-the-center-theorem\">Circle Theorem 2: Central Angle Theorem (The Angle at the Center Theorem)<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-db17710b-10b8-4e53-a05b-29585ea3a43f\">\n\n\n<p><strong>Central Angle Theorem: <\/strong>The central angle subtended by two points on a circle is always twice the inscribed angle subtended by those points.<\/p>\n\n\n<\/div>\n\n\n<p>Here, the angle BAC is known as the <strong>inscribed angle, <\/strong>an angle made from points lying on the circle&#8217;s circumference.<\/p>\n\n\n\n<p>The angle BOC is the <strong>central angle,<\/strong> an angle whose vertex is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points B and C.<\/p>\n\n\n\n<p>Thus, the theorem states that an inscribed angle \u2220BAC = x\u00b0 is half of the measure of the central angle \u2220BOC = 2x\u00b0.<\/p>\n\n\n\n<p>\u2220BOC = 2 \u2220BAC.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"373\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-i.png\" alt=\"Angle at the center theorem\" class=\"wp-image-33664\" title=\"Angle at the center theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-i.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-i-300x180.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-circle-theorem-3-angles-in-the-same-segment-theorem\">Circle Theorem 3: Angles in the Same Segment Theorem<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-14599762-e0ff-4b1b-91c7-fc9fa3d97fbd\">\n\n\n<p><strong>Angles in the same segment theorem: <\/strong>Angles formed in the same segment (either major segment or minor segment) of a circle are equal.<\/p>\n\n\n<\/div>\n\n\n<p>Here, according to the angles in the same segment theorem: \u2220BAD = \u2220BCD<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"316\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-ii.png\" alt=\"Angles in the same segment theorem\" class=\"wp-image-33665\" title=\"Angles in the same segment theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-ii.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-ii-300x153.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-circle-theorem-4-angle-in-a-semicircle-theorem\">Circle Theorem 4: Angle in a Semicircle Theorem<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-836fd63a-feff-415c-b751-7b47524b71fe\">\n\n\n<p><strong>Angle in a semicircle theorem: <\/strong>An angle in a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/half-circle\">semicircle<\/a> is always a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/right-angle\">right angle<\/a> (measures 90 degrees).<\/p>\n\n\n<\/div>\n\n\n<p>In other words, an angle subtended by a circle&#8217;s diameter is always a right angle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"350\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-iii.png\" alt=\"Angle in a semicircle is always 90 degrees\" class=\"wp-image-33667\" title=\"Angle in a semicircle is always 90 degrees\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-iii.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-iii-300x169.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Here, according to the angle in a semicircle theorem: \u2220A = \u2220B = \u2220C = 90<sup>0<\/sup><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"271\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-iii-a.png\" alt=\"Angles A, B, C in a semicircle are right angles\" class=\"wp-image-33668\" title=\"Angles A, B, C in a semicircle are right angles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-iii-a.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-iii-a-300x131.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-circle-theorem-5-chord-of-a-circle-theorem\">Circle Theorem 5: Chord of a Circle Theorem<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-ee63b209-4b3f-41ce-969a-0dfc72cb8d7b\">\n\n\n<p><strong>Chord of a circle theorem: <\/strong>The perpendicular drawn from the center of the circle to a chord bisects the chord.<\/p>\n\n\n<\/div>\n\n\n<p>Here, according to the chord of a circle theorem, we have&nbsp;<\/p>\n\n\n\n<p>\u2220OPA = \u2220OPB = 90<sup>0<\/sup><\/p>\n\n\n\n<p>AP = PB<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"347\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-iv.png\" alt=\"Chord of a circle theorem\" class=\"wp-image-33669\" title=\"Chord of a circle theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-iv.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-iv-300x168.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-circle-theorem-6-angles-subtended-by-equal-chords-theorem\">Circle Theorem 6: Angles Subtended by Equal Chords Theorem<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-236a0cb6-0067-4725-af43-7964197ddb46\">\n\n\n<p><strong>Angles subtended by equal chords theorem: <\/strong>Two equal chords of a circle subtend equal angles at the center of the circle.<\/p>\n\n\n<\/div>\n\n\n<p>The converse is also true. If two angles subtended at the center by two chords are equal, then the chords are of equal length.<\/p>\n\n\n\n<p>In the given diagram, the chords XY and ST are equal. Thus, the angles subtended by them are also equal.<\/p>\n\n\n\n<p>\u2220AOB = \u2220POQ<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"396\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-v.png\" alt=\"Angles subtended by equal chords are equal.\" class=\"wp-image-33670\" title=\"Angles subtended by equal chords are equal.\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-v.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-v-300x192.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-circle-theorem-7-cyclic-quadrilateral-theorem\">Circle Theorem 7: Cyclic Quadrilateral Theorem<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-e117c529-7855-4874-bcbb-b5b0d50d4a2d\">\n\n\n<p><strong>Cyclic quadrilateral theorem: <\/strong>The sum of opposite angles in a cyclic quadrilateral is equal to 180<sup>0<\/sup>.<\/p>\n\n\n<\/div>\n\n\n<p>A cyclic quadrilateral is a quadrilateral where all four vertices lie on a circle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"419\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-vi.png\" alt=\"Cyclic quadrilateral ABCD\" class=\"wp-image-33671\" title=\"Cyclic quadrilateral ABCD\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-vi.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-vi-300x203.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Here, ABCD is a cyclic quadrilateral. According to the cyclic quadrilateral theorem:&nbsp;<\/p>\n\n\n\n<p>\u2220A + \u2220C = <strong>180<\/strong><sup>0<\/sup> and \u2220B + \u2220D = <strong>180<\/strong><sup>0<\/sup><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-circle-theorem-8-tangent-of-a-circle-theorem-1\">Circle Theorem 8: Tangent of a Circle Theorem-1<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-205d2960-f0c8-4391-966d-2951d54a9d03\">\n\n\n<p><strong>Tangent of a circle theorem-1:<\/strong> The tangent makes a right angle with the radius of a circle at the point of tangency.<\/p>\n\n\n<\/div>\n\n\n<p>In the given diagram, the radius OP is perpendicular to the tangent AB.&nbsp;<\/p>\n\n\n\n<p>OP \u22a5 AB.<\/p>\n\n\n\n<p>\u2220OPA = \u2220OPB = <strong>90<sup>0<\/sup><\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"366\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-vii.png\" alt=\"Tangent of a circle theorem\" class=\"wp-image-33672\" title=\"Tangent of a circle theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-vii.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-vii-300x177.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-circle-theorem-9-two-tangents-theorem\">Circle Theorem 9: Two Tangents Theorem<\/h2>\n\n\n\n<p>If two tangent lines PA and PB are drawn from an external point, then<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Two tangents have the same length. <strong>(PA = PB)<\/strong><\/li>\n\n\n\n<li>The two tangents subtend equal angles at the center of the circle.<strong> (\u2220POA = \u2220POB)<\/strong><\/li>\n\n\n\n<li>The line that connects the exterior point to the center will divide the angle between the tangents into two equal angles.<strong> (\u2220OPA = \u2220OPB)<\/strong><\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"450\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-viii.png\" alt=\"Tangent of a circle theorem\" class=\"wp-image-33673\" title=\"Tangent of a circle theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-viii.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-viii-300x218.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"12-circle-theorems-formulas\">Circle Theorems Formulas<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th><strong>Theorems<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Shapes<\/strong><\/th><th><strong>Formula<\/strong><\/th><\/tr><\/thead><tbody><tr><td><strong>Alternate Segment Theorem<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" width=\"350\" height=\"327\" class=\"wp-image-33674\" style=\"width: 350px;\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/alternate-segment-theorem.png\" alt=\"Alternate segment theorem\"><\/td><td>\u2220x = \u2220y\u00a0<br>and<br>\u2220a = \u2220b<\/td><\/tr><tr><td>The central angle subtended by two points on a circle is always twice the inscribed angle subtended by those points.<br><\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" width=\"350\" height=\"347\" class=\"wp-image-33675\" style=\"width: 350px;\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/central-angle-theorem.png\" alt=\"Central angle theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/central-angle-theorem.png 228w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/central-angle-theorem-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/central-angle-theorem-120x120.png 120w\" sizes=\"auto, (max-width: 350px) 100vw, 350px\" \/><\/td><td>\u2220BOC = 2\u2220BAC<\/td><\/tr><tr><td>Angles in the same segment are congruent.<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" width=\"350\" height=\"342\" class=\"wp-image-33676\" style=\"width: 350px;\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/angles-in-the-same-segment-theorem.png\" alt=\"angles in the same segment theorem\"><\/td><td>\u2220PRQ = \u2220PSQ<\/td><\/tr><tr><td>Angles in a semicircle are right angles.<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" width=\"350\" height=\"244\" class=\"wp-image-33677\" style=\"width: 350px;\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/angles-in-a-semicircle-theorem.png\" alt=\"angles in a semicircle theorem\"><\/td><td>\u2220A = \u2220B = \u2220C = <strong>90<\/strong><sup>0<\/sup><\/td><\/tr><tr><td>Chord of a circle theorem<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" width=\"400\" height=\"312\" class=\"wp-image-33678\" style=\"width: 400px;\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/chord-of-a-circle-theorem.png\" alt=\"chord of a circle theorem\"><\/td><td>       AP = PB<br>\u2220OPA = \u2220OPB = <strong>90<\/strong><sup>0<\/sup>\u00a0<\/td><\/tr><tr><td>Angles subtended by equal chords<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" width=\"350\" height=\"337\" class=\"wp-image-33679\" style=\"width: 350px;\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/angles-subtended-by-equal-chords.png\" alt=\"Angles subtended by equal chords\"><\/td><td>\u2220XOY = \u2220SOT<\/td><\/tr><tr><td>Cyclic quadrilateral theorem<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" width=\"350\" height=\"381\" class=\"wp-image-33680\" style=\"width: 350px;\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/cyclic-quadrilateral-theorem.png\" alt=\"Cyclic quadrilateral theorem\"><\/td><td>\u2220A + \u2220C = <strong>180<\/strong><sup>0<\/sup>\u00a0and\u00a0\u2220B + \u2220D = <strong>180<\/strong><sup><sup>0<\/sup><\/sup><\/td><\/tr><tr><td>Tangent of a circle theorem-1<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" width=\"350\" height=\"273\" class=\"wp-image-33681\" style=\"width: 350px;\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/tangent-makes-a-right-angle-with-the-radius-.png\" alt=\"Tangent makes a right angle with the radius\u00a0\"><\/td><td>\u2220OPA = \u2220OPB = <strong>90<\/strong><sup>0<\/sup><\/td><\/tr><tr><td>Tangent of a circle theorem-2<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" width=\"400\" height=\"226\" class=\"wp-image-33682\" style=\"width: 400px;\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/tangent-of-a-circle-theorem-.png\" alt=\"Tangent of a circle theorem\u00a0\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/tangent-of-a-circle-theorem-.png 421w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/tangent-of-a-circle-theorem--300x170.png 300w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/td><td>PA = PB\u2220POA = \u2220POB\u2220OPA = \u2220OPB<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"13-facts-about-circle-theorems\">Facts about Circle Theorems<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>The first theorems based on the circles are attributed to Thales around 650 BC.<\/li>\n\n\n\n<li>In the fields of engineering and design, the circle theorems have important applications.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"14-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we delved into the essential circle theorems that provide valuable insights into angles, arcs, and their relationships within a circle. Understanding these theorems is crucial for various geometric applications. Now, let&#8217;s reinforce our knowledge by tackling examples and practicing MCQs for better comprehension.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"15-solved-examples-on-circle-theorems\">Solved Examples on Circle Theorems<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>In the circle given below, triangle ABC is inscribed in the circle and the tangent DE meets the circle at the point B. Find the measure of angle \u201cx\u201d and \u201cy.\u201d<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"253\" height=\"215\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-problem-i.png\" alt=\"Alternate segment theorem example\" class=\"wp-image-33683\" title=\"Alternate segment theorem example\"\/><\/figure>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>We know that the sum of interior angles of a triangle is equal to <strong>18<\/strong><strong>0<\/strong>.&nbsp;<\/p>\n\n\n\n<p>\u2220BAC + \u2220ACB + \u2220ABC = <strong>180<\/strong><sup>0<\/sup><\/p>\n\n\n\n<p>x + <strong>57<\/strong><sup>0<\/sup> +\u00a0 <strong>48<\/strong><sup>0<\/sup> = <strong>180<\/strong><sup>0<\/sup><\/p>\n\n\n\n<p>x = <strong>180<\/strong><sup>0<\/sup> \u2013 <strong>105<\/strong><sup>0<\/sup><\/p>\n\n\n\n<p>x = <strong>75<\/strong><sup>0<\/sup><\/p>\n\n\n\n<p>Now, according to the alternate segment theorem, the angle formed between the tangent and the chord through the point of contact of the tangent is equal to the angle formed by the same chord in the alternate segment.<\/p>\n\n\n\n<p>x = y = <strong>75<\/strong><sup>0<\/sup><\/p>\n\n\n\n<p>Hence, the measure of \u2220x and \u2220y is <strong>75<\/strong><sup>0<\/sup>.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li><strong>In the figure given below, find the value of x using the circle theorems.<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"235\" height=\"207\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-problem-ii.png\" alt=\"Angles in a semicircle theorem example\" class=\"wp-image-33684\" title=\"Angles in a semicircle theorem example\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>In the given figure, \u2220ABC is an angle in a semicircle.&nbsp;<\/p>\n\n\n\n<p>Angle in a semicircle is always a right angle.&nbsp;<\/p>\n\n\n\n<p>Thus, m\u2220ABC = <strong>90<\/strong><sup>0<\/sup><\/p>\n\n\n\n<p>We know that the sum of interior angles of a triangle is equal to <strong>180<\/strong><sup>0<\/sup>.\u00a0<\/p>\n\n\n\n<p>m\u2220BAC + m\u2220ACB + m\u2220ABC = <strong>180<\/strong><sup>0<\/sup><\/p>\n\n\n\n<p>x + <strong>37<\/strong><sup>0<\/sup> + <strong>90<\/strong><sup>0<\/sup> = <strong>180<\/strong><sup>0<\/sup><\/p>\n\n\n\n<p>x + <strong>127<\/strong><sup><sup>0<\/sup> <\/sup>= <strong>180<\/strong><sup>0<\/sup><\/p>\n\n\n\n<p>x = <strong>180<\/strong><sup>0<\/sup> \u2212 <strong>127<\/strong><sup>0<\/sup> = <strong>53<\/strong><sup>0<\/sup><\/p>\n\n\n\n<p>Hence, the value of x is <strong>53<\/strong><sup>0<\/sup>.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li><strong>In the figure given below, find the value of x using the circle theorems.<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"229\" height=\"232\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-problem-iii.png\" alt=\"Example of angle at the center theorem\" class=\"wp-image-33685\" title=\"Example of angle at the center theorem\"\/><\/figure>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>According to \u201cthe angle at the center theorem,\u201d the central angle subtended by two points on a circle is always twice the inscribed angle subtended by those points.<\/p>\n\n\n\n<p>\u2220AOB = 2\u2220ACB.<\/p>\n\n\n\n<p>x = 2 \u00d7 <strong>47<\/strong><sup>0<\/sup> = <strong>94<\/strong><sup>0<\/sup><\/p>\n\n\n\n<p>The value of x is <strong>94<\/strong><sup>0<\/sup>.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n<li><strong>In the given figure, the point O is a center of a circle, the radius of a circle is 17 inches and OP = 8 inches. Find the length of the chord AB.<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"242\" height=\"233\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-problem-iv.png\" alt=\"Example of a chord of a circle theorem\" class=\"wp-image-33687\" title=\"Example of a chord of a circle theorem\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>In the given figure,&nbsp;<\/p>\n\n\n\n<p>OA = OB = 17 inches&nbsp;<\/p>\n\n\n\n<p>OP = 8 inches<\/p>\n\n\n\n<p>OP\u22a5 AB<\/p>\n\n\n\n<p>Using pythagoras theorem in triangle OPB, we get<\/p>\n\n\n\n<p>OP<sup>2<\/sup> + PB<sup>2<\/sup> = OB<sup>2<\/sup><\/p>\n\n\n\n<p>8<sup>2<\/sup> + PB<sup>2<\/sup> = 17<sup>2<\/sup><\/p>\n\n\n\n<p>PB<sup>2<\/sup> = 17<sup>2<\/sup> \u2212 8<sup>2<\/sup> = 225<\/p>\n\n\n\n<p>Therefore, PB = $\\sqrt{225}$ = 15 inches<\/p>\n\n\n\n<p>According to the chord of a circle theorem, the perpendicular drawn from the center of the circle bisects the chord.<\/p>\n\n\n\n<p>Thus, AP = PB<\/p>\n\n\n\n<p>\u2234 AB = AP + PB = 15 inches + 15 inches = 30 inches.<\/p>\n\n\n\n<p>Hence, the length of the chord AB is 30 inches.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"5\">\n<li><strong>Find the value of \u201cx\u201d and \u201cy\u201d using the cyclic quadrilateral theorem.<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"207\" height=\"189\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-problem-v.png\" alt=\"Example on cyclic quadrilateral theorem\" class=\"wp-image-33689\" title=\"Example on cyclic quadrilateral theorem\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>In the given figure, ABCD is cyclic quadrilateral.&nbsp;<\/p>\n\n\n\n<p>We know that the sum of opposite angles in a cyclic quadrilateral is equal to <strong>180<\/strong><sup>0<\/sup>.<\/p>\n\n\n\n<p>So, x + <strong>98<sup>0<\/sup><\/strong> = <strong>180<\/strong><sup>0<\/sup><\/p>\n\n\n\n<p>\u00a0x = <strong>180<\/strong><sup>0<\/sup> \u2212 <strong>98<\/strong><sup>0<\/sup> = <strong>82<\/strong><sup>0<\/sup><\/p>\n\n\n\n<p>Similarly,<\/p>\n\n\n\n<p>y + <strong>95<\/strong><sup>0<\/sup> = <strong>180<\/strong><sup>0<\/sup><\/p>\n\n\n\n<p>\u00a0x = <strong>180<sup>0<\/sup><\/strong> \u2212 <strong>95<\/strong><sup>0<\/sup> = <strong>85<\/strong><sup>0<\/sup><\/p>\n\n\n\n<p>The values of x and y are <strong>82<\/strong> and <strong>85<\/strong> respectively.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"6\">\n<li><strong>Find the value of \u201cx\u201d in the figure given below.<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"467\" height=\"248\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-problem-vi.png\" alt=\"Tangent to a circle theorem example\" class=\"wp-image-33691\" title=\"Tangent to a circle theorem example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-problem-vi.png 467w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circle-theorem-problem-vi-300x159.png 300w\" sizes=\"auto, (max-width: 467px) 100vw, 467px\" \/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Two tangent lines PA and PB are drawn from an external point \u201cP\u201d as shown in the figure, then two tangents have the same length.<\/p>\n\n\n\n<p>Thus, PA = PB.<\/p>\n\n\n\n<p>x<sup>2<\/sup> + 10 = 46<\/p>\n\n\n\n<p>x<sup>2<\/sup> = 46 \u2212 10<\/p>\n\n\n\n<p>x<sup>2<\/sup> = 36<\/p>\n\n\n\n<p>x = 6<\/p>\n\n\n\n<p>Hence, the value of \u201cx\u201d is 6.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"16-practice-problems-on-circle-theorems\">Practice Problems on Circle Theorems<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Circle Theorems: Definition, Formulas, Steps, Examples, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">The angle subtended by a diameter at any point of the circumference is equal to _______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$45^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$60^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$90^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$180^{\\circ}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $90^{\\circ}$<br\/>The angle subtended by a diameter at any point of the circumference is equal to $90^{\\circ}$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">If the inscribed angle is $50^{\\circ}$, then the central angle is ________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$50^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$100^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$110^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$25^{\\circ}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $100^{\\circ}$<br\/>We know that the inscribed angle is half of the measure of the central angle.<br>\r\nCentral angle $= 2 \\times 50^{\\circ} = 100^{\\circ}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">The opposite angles in a cyclic quadrilateral are ______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">complementary<\/div><div class=\"spq_answer_block\" data-value=\"1\">equal<\/div><div class=\"spq_answer_block\" data-value=\"2\">supplementary<\/div><div class=\"spq_answer_block\" data-value=\"3\">right angles<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: supplementary<br\/>The opposite angles in a cyclic quadrilateral are supplementary. They add up to $180^{\\circ}$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Angles formed in the same segment of a circle are ______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">equal<\/div><div class=\"spq_answer_block\" data-value=\"1\">different<\/div><div class=\"spq_answer_block\" data-value=\"2\">right angles<\/div><div class=\"spq_answer_block\" data-value=\"3\">none of these<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: equal<br\/>Angles formed in the same segment of a circle are always equal.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", 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subtended by a diameter at any point of the circumference is equal to _______.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The angle subtended by a diameter at any point of the circumference is equal to $$90^{\\\\circ}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$45^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The angle subtended by a diameter at any point of the circumference is equal to $$90^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$60^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The angle subtended by a diameter at any point of the circumference is equal to $$90^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$180^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The angle subtended by a diameter at any point of the circumference is equal to $$90^{\\\\circ}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$90^{\\\\circ}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The angle subtended by a diameter at any point of the circumference is equal to $$90^{\\\\circ}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The angle subtended by a diameter at any point of the circumference is equal to $$90^{\\\\circ}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the inscribed angle is $$50^{\\\\circ}$$, then the central angle is ________.\",\n                    \"text\": \"If the inscribed angle is $$50^{\\\\circ}$$, then the central angle is ________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We know that the inscribed angle is half of the measure of the central angle.<br>\r\nCentral angle $$= 2 \\\\times 50^{\\\\circ} = 100^{\\\\circ}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$50^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the inscribed angle is half of the measure of the central angle.<br>\r\nCentral angle $$= 2 \\\\times 50^{\\\\circ} = 100^{\\\\circ}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$110^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the inscribed angle is half of the measure of the central angle.<br>\r\nCentral angle $$= 2 \\\\times 50^{\\\\circ} = 100^{\\\\circ}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$25^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the inscribed angle is half of the measure of the central angle.<br>\r\nCentral angle $$= 2 \\\\times 50^{\\\\circ} = 100^{\\\\circ}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$100^{\\\\circ}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We know that the inscribed angle is half of the measure of the central angle.<br>\r\nCentral angle $$= 2 \\\\times 50^{\\\\circ} = 100^{\\\\circ}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We know that the inscribed angle is half of the measure of the central angle.<br>\r\nCentral angle $$= 2 \\\\times 50^{\\\\circ} = 100^{\\\\circ}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The opposite angles in a cyclic quadrilateral are ______.\",\n                    \"text\": \"The opposite angles in a cyclic quadrilateral are ______.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The opposite angles in a cyclic quadrilateral are supplementary. They add up to $$180^{\\\\circ}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"complementary\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The opposite angles in a cyclic quadrilateral are supplementary. They add up to $$180^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"equal\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The opposite angles in a cyclic quadrilateral are supplementary. They add up to $$180^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"right angles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The opposite angles in a cyclic quadrilateral are supplementary. They add up to $$180^{\\\\circ}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"supplementary\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The opposite angles in a cyclic quadrilateral are supplementary. They add up to $$180^{\\\\circ}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The opposite angles in a cyclic quadrilateral are supplementary. They add up to $$180^{\\\\circ}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Angles formed in the same segment of a circle are ______.\",\n                    \"text\": \"Angles formed in the same segment of a circle are ______.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Angles formed in the same segment of a circle are always equal.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"different\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Angles formed in the same segment of a circle are always equal.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"right angles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Angles formed in the same segment of a circle are always equal.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"none of these\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Angles formed in the same segment of a circle are always equal.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"equal\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Angles formed in the same segment of a circle are always equal.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Angles formed in the same segment of a circle are always equal.\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"17-frequently-asked-questions-on-circle-theorems\">Frequently Asked Questions on Circle Theorems<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-9678dc5b-66af-4354-9709-e6a2b8d98bd6\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-9678dc5b-66af-4354-9709-e6a2b8d98bd6\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9678dc5b-66af-4354-9709-e6a2b8d98bd6\"><strong>Why are circle theorems important?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-9678dc5b-66af-4354-9709-e6a2b8d98bd6\">\n\n<p>Geometry problems can be solved with the help of circle theorems. There are a number of useful patterns and theorems that can be deduced from drawing angles and lines inside a circle, which we can use in both practical and theoretical situations.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-9678dc5b-66af-4354-9709-e6a2b8d98bd6\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9678dc5b-66af-4354-9709-e6a2b8d98bd6\"><strong>How to find angles using circle theorems?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-9678dc5b-66af-4354-9709-e6a2b8d98bd6\">\n\n<p>To find <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/angle\">angles<\/a> using the circle theorems based on a given condition and shape, we can apply circle theorems based on angles. Some important circle theorems based on angles are as follows:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The measure of angles subtended by an arc at the center of a circle is equal to twice the angles at any point on the circumference of the circle from the same arc.<\/li>\n\n\n\n<li>Angles formed in the same segment of a circle are equal.<\/li>\n\n\n\n<li>The angle in a semicircle is always 90 degrees.<\/li>\n<\/ul>\n\n\n\n<p>The sum of opposite angles in a cyclic quadrilateral is equal to 180<sup>0<\/sup>.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-9678dc5b-66af-4354-9709-e6a2b8d98bd6\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9678dc5b-66af-4354-9709-e6a2b8d98bd6\"><strong>Why is it called a circle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-9678dc5b-66af-4354-9709-e6a2b8d98bd6\">\n\n<p>The word circle is derived from the Greek word <em>kirkos<\/em>, meaning hoop or ring.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-9678dc5b-66af-4354-9709-e6a2b8d98bd6\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9678dc5b-66af-4354-9709-e6a2b8d98bd6\"><strong>List the circle theorems.<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-9678dc5b-66af-4354-9709-e6a2b8d98bd6\">\n\n<p>Following are the list of circle theorems:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Alternate segment theorem<\/li>\n\n\n\n<li>The angle at the center theorem<\/li>\n\n\n\n<li>Angles in the same segment theorem<\/li>\n\n\n\n<li>Angle in a semicircle theorem<\/li>\n\n\n\n<li>Chord of a circle theorem<\/li>\n\n\n\n<li>Cyclic quadrilateral theorem<\/li>\n\n\n\n<li>Tangent of a circle theorems<\/li>\n<\/ol>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-9678dc5b-66af-4354-9709-e6a2b8d98bd6\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9678dc5b-66af-4354-9709-e6a2b8d98bd6\"><strong>What is a cyclic quadrilateral?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-9678dc5b-66af-4354-9709-e6a2b8d98bd6\">\n\n<p>A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/quadrilateral\">quadrilateral<\/a> with all four vertices lying on a circle is known as a cyclic quadrilateral. Sometimes, It is also known as the inscribed quadrilateral. The sum of opposite angles in a cyclic quadrilateral is equal to 180<sup>0<\/sup>.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-5-9678dc5b-66af-4354-9709-e6a2b8d98bd6\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9678dc5b-66af-4354-9709-e6a2b8d98bd6\"><strong>What is the sum of all angles of a cyclic quadrilateral?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-5-9678dc5b-66af-4354-9709-e6a2b8d98bd6\">\n\n<p>As we know that the sum of all angles of a quadrilateral is equal to 360<sup>0<\/sup>. Hence, the sum of all angles of a cyclic quadrilateral is also equal to 360<sup>0<\/sup>.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are Circle Theorems in Geometry? The circle theorems in geometry are statements that prove significant results about circles. These theorems provide important information or facts about various parts of a circle.&nbsp; We can use circle theorems and previous knowledge of properties of a circle to calculate missing angles. The circle angle theorems give us &#8230; <a title=\"Circle Theorems: Definition, Formulas, Steps, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/circle-theorems\" aria-label=\"More on Circle Theorems: Definition, Formulas, Steps, Examples, FAQs\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-33652","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33652","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=33652"}],"version-history":[{"count":9,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33652\/revisions"}],"predecessor-version":[{"id":33699,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33652\/revisions\/33699"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=33652"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=33652"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=33652"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}