{"id":5360,"date":"2026-06-25T13:26:45","date_gmt":"2026-06-25T07:56:45","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=5360"},"modified":"2026-06-25T13:26:49","modified_gmt":"2026-06-25T07:56:49","slug":"ncert-class-9-maths-chapter-5-exercise-5-2-solutions-circles","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/ncert-class-9-maths-chapter-5-exercise-5-2-solutions-circles\/","title":{"rendered":"NCERT Class 9 Maths Chapter 5 Exercise 5.2 Solutions | Circles"},"content":{"rendered":"<div class=\"mymoc-top mymoc-entity-placement\" id=\"mymoc-764593039\"><div id=\"mymoc-3198780120\"><a href=\"https:\/\/amzn.to\/43YYZi3\" aria-label=\"smart-phones\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smart-phones.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smart-phones.png 1303w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smart-phones-300x76.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smart-phones-1024x259.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smart-phones-768x194.png 768w\" sizes=\"(max-width: 1303px) 100vw, 1303px\" width=\"1303\" height=\"329\"><\/a><\/div><\/div><div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/5360?print=print\" class=\"pdfprnt-button pdfprnt-button-print\" target=\"_blank\"><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/print.png\" alt=\"image_print\" title=\"Print Content\"><span class=\"pdfprnt-button-title pdfprnt-button-print-title\">Print<\/span><\/a> <span class=\"pdfprnt-count-generation\">3<\/span><\/div>\n<h1 class=\"wp-block-heading\">Short Introduction<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Exercise 5.2 of Chapter 5, <strong>I&rsquo;m Up and Down, and Round and Round<\/strong>, introduces important properties of chords and circles. In this exercise, students learn that the triangle formed by joining a chord to the centre of a circle is an isosceles triangle and how equal chords lead to congruent triangles. These concepts are fundamental for understanding advanced circle theorems.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Quick Information Box<\/h1>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Particular<\/th><th>Details<\/th><\/tr><\/thead><tbody><tr><td>Class<\/td><td>9<\/td><\/tr><tr><td>Subject<\/td><td>Mathematics<\/td><\/tr><tr><td>Chapter<\/td><td>5 &ndash; I&rsquo;m Up and Down, and Round and Round<\/td><\/tr><tr><td>Exercise<\/td><td>5.2<\/td><\/tr><tr><td>Topic<\/td><td>Chords and Angles Subtended by Chords<\/td><\/tr><tr><td>Difficulty Level<\/td><td>Easy to Moderate<\/td><\/tr><tr><td>Important Concepts<\/td><td>Radius, Chord, Isosceles Triangle, Congruence<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Concepts Used (Topics Covered)<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Definition of a Circle<\/li>\n\n\n\n<li>Radius and Chord<\/li>\n\n\n\n<li>Isosceles Triangle<\/li>\n\n\n\n<li>SSS Congruence Criterion<\/li>\n\n\n\n<li>Equal Chords of a Circle<\/li>\n\n\n\n<li>Congruent Triangles<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Important Formulas and Facts<\/h1>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>All radii of the same circle are equal.<\/strong><\/li>\n\n\n\n<li>If two sides of a triangle are equal, then the triangle is an <strong>isosceles triangle<\/strong>.<\/li>\n\n\n\n<li><strong>SSS Congruence Criterion:<\/strong><br>If three sides of one triangle are equal to the corresponding three sides of another triangle, then the triangles are congruent.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Exercise 5.2 Solutions<\/h1>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Question 1<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Show that the triangle formed by a chord and the centre of the circle is isosceles.<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img fetchpriority=\"high\" decoding=\"async\" width=\"793\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-232-793x1024.png\" alt=\"\" class=\"wp-image-5426\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-232-793x1024.png 793w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-232-232x300.png 232w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-232-768x991.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-232.png 1104w\" sizes=\"(max-width: 793px) 100vw, 793px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Question 2<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Show that if two such isosceles triangles (occurring in the previous question) have equal base length, they are congruent to each other.<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"819\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-233-819x1024.png\" alt=\"\" class=\"wp-image-5430\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-233-819x1024.png 819w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-233-240x300.png 240w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-233-768x960.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-233.png 1122w\" sizes=\"(max-width: 819px) 100vw, 819px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Common Mistakes<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">&#10060; Forgetting that all radii of a circle are equal.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10060; Using SAS congruence instead of SSS.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10060; Not mentioning the reason that OA, OB, OC and OD are radii.<\/p>\n\n\n\n<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/class-9-maths-exercise-1-1-solutions-coordinate-geometry-ncert-solutions\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">Class 9 Maths Exercise 1.1 Solutions | Coordinate Geometry NCERT Solutions<\/span><\/a><\/div><p class=\"wp-block-paragraph\">&#10060; Writing only the answer without proving the theorem.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Exam Tips<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">&#10004; Always draw a neat labelled figure.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10004; Mention the theorem or congruence criterion used.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10004; Write statements and reasons separately.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10004; Remember: <strong>Equal radii &rarr; Isosceles triangle.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Practice MCQs<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">1. The triangle formed by a chord and the centre of a circle is:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. Scalene<br>B. Right-angled<br>C. Isosceles<br>D. Equilateral<\/p>\n\n\n\n<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/class-9-maths-exercise-1-2-solutions-coordinate-geometry-ncert-solutions\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">NCERT Class 9 Maths Exercise 1.2 Solutions | Coordinate Geometry NCERT Solutions<\/span><\/a><\/div><p class=\"wp-block-paragraph\"><strong>Answer:<\/strong> C. Isosceles<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">2. Which criterion is used in Question 2?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. RHS<br>B. SAS<br>C. ASA<br>D. SSS<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answer:<\/strong> D. SSS<\/p><div class=\"mymoc-middle mymoc-entity-placement\" id=\"mymoc-1367469897\"><div id=\"mymoc-724058953\"><a href=\"https:\/\/amzn.to\/3S4CntS\" aria-label=\"Stationeries\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/Stationeries.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/Stationeries.png 1303w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/Stationeries-300x89.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/Stationeries-1024x304.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/Stationeries-768x228.png 768w\" sizes=\"(max-width: 1303px) 100vw, 1303px\" width=\"1080\" height=\"100\"><\/a><\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">3. A chord joins two points on a circle. The segments joining these points to the centre are:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. Unequal<br>B. Radii<br>C. Diameters<br>D. Tangents<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answer:<\/strong> B. Radii<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">4. If two chords are equal, then the corresponding triangles formed with the centre are:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. Similar<br>B. Congruent<br>C. Scalene<br>D. Right-angled<\/p>\n\n\n\n<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/class-9-maths-end-of-chapter-exercise-solutions-coordinate-geometry-ncert-solutions\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">NCERT Class 9 Maths End of Chapter Exercise Solutions | Coordinate Geometry<\/span><\/a><\/div><p class=\"wp-block-paragraph\"><strong>Answer:<\/strong> B. Congruent<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Frequently Asked Questions (FAQs)<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">Q1. Why is the triangle formed by a chord and the centre always isosceles?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Because the two sides joining the centre to the endpoints of the chord are radii and hence equal.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Q2. Which congruence theorem is used in Exercise 5.2 Question 2?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The <strong>SSS Congruence Criterion<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Q3. Are all triangles formed by chords and the centre congruent?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">No. They are congruent only when the chords are equal.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Q4. Why are radii important in circle geometry?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Most circle theorems are based on the fact that all radii of a circle are equal.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Final Answer Summary<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Question 1:<\/strong> The triangle formed by a chord and the centre is <strong>isosceles<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Question 2:<\/strong> Two such triangles with equal base lengths are <strong>congruent by SSS criterion<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<p class=\"wp-block-paragraph\">&#128218; Looking for more NCERT Maths solutions and chapter-wise explanations?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Visit <strong><a href=\"http:\/\/www.mymockmate.com\/\">www.mymockmate.com<\/a><\/strong> for:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; Complete NCERT Solutions<br>&#9989; Step-by-Step Explanations<br>&#9989; Practice Questions and MCQs<br>&#9989; Exam Preparation Notes<br>&#9989; Chapter-wise Important Questions<\/p>\n<div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/5360?print=print\" class=\"pdfprnt-button pdfprnt-button-print\" target=\"_blank\"><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/print.png\" alt=\"image_print\" title=\"Print Content\"><span class=\"pdfprnt-button-title pdfprnt-button-print-title\">Print<\/span><\/a> <span class=\"pdfprnt-count-generation\">3<\/span><\/div>\n    <div class=\"xs_social_share_widget xs_share_url after_content \t\tmain_content  wslu-style-1 wslu-share-box-shaped wslu-fill-colored wslu-none wslu-share-horizontal wslu-theme-font-no wslu-main_content\">\n\n\t\t\n        <ul>\n\t\t\t        <\/ul>\n    <\/div> \n<div class=\"mymoc-bottom mymoc-entity-placement\" id=\"mymoc-3324236970\"><div id=\"mymoc-390100088\"><a href=\"https:\/\/amzn.to\/4xnw9oY\" aria-label=\"head-phones\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/head-phones.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/head-phones.png 1301w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/head-phones-300x80.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/head-phones-1024x274.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/head-phones-768x205.png 768w\" sizes=\"(max-width: 1301px) 100vw, 1301px\" width=\"1301\" height=\"348\"><\/a><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p> 3 Short Introduction Exercise 5.2 of Chapter 5, I&rsquo;m Up and Down, and Round and Round, introduces<\/p>\n","protected":false},"author":1,"featured_media":5363,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[4,11],"tags":[3569,1188,3570,3571,3573,1170,3572,2432,53],"class_list":["post-5360","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-9","category-maths-class-9","tag-chapter-5-exercise-5-2-solutions","tag-circle-theorems","tag-circles","tag-equal-chords","tag-ganita-manjari-class-9","tag-geometry-solutions","tag-isosceles-triangle","tag-ncert-class-9-maths","tag-ncert-maths-solutions"],"featured_image_src":"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/NCERT-Class-9-Maths-Chapter-5-Exercise-5.2-Solutions.png","author_info":{"display_name":"Team Mymockmate","author_link":"https:\/\/mymockmate.com\/notes\/author\/bsm_adm\/"},"jetpack_publicize_connections":[],"_links":{"self":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/5360","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/comments?post=5360"}],"version-history":[{"count":4,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/5360\/revisions"}],"predecessor-version":[{"id":5433,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/5360\/revisions\/5433"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/5363"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=5360"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=5360"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=5360"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}