{"id":4518,"date":"2023-02-15T05:08:08","date_gmt":"2023-02-15T05:08:08","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=4518"},"modified":"2023-02-15T05:13:23","modified_gmt":"2023-02-15T05:13:23","slug":"ncert-solutions-class-9-maths-chapter-10-circles-ex-10-2","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-10-circles-ex-10-2\/","title":{"rendered":"NCERT Solutions Class 9 Maths Chapter 10 Circles Ex 10.2"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 9 Maths\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 10 (Circles)\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 9 Mathematics\u00a0<strong>Chapter &#8211; 10 Circles <\/strong>Exercise 10.2 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>Chapter 10: Circles<\/strong><\/span><\/p>\n<ul>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-10-circles-ex-10-1\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 10.1<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-10-circles-ex-10-3\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 10.3<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-10-circles-ex-10-4\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 10.4<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-10-circles-ex-10-5\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 10.5<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-10-circles-ex-10-6\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 10.6<\/a><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 10.2<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.<br \/>\n<\/strong><strong>Answer &#8211;\u00a0<\/strong>Let QR and YZ be the equal chords of 2 congruent circles.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-4529\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.2-Ans2.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"378\" height=\"177\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.2-Ans2.png 795w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.2-Ans2-300x140.png 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.2-Ans2-768x359.png 768w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.2-Ans2-480x225.png 480w\" sizes=\"auto, (max-width: 378px) 100vw, 378px\" \/><br \/>\nLet QR and YZ be the equal chords of 2 congruent circles.<\/span><br \/>\n<span style=\"color: #000000;\">Then, QR = YZ<\/span><br \/>\n<span style=\"color: #000000;\">We need to prove that they subtend equal angles at the center. That is, \u2220QPR = \u2220YXZ<\/span><br \/>\n<span style=\"color: #000000;\">We know that the radii of both circles are equal. So, we get: PR = PQ = XZ = XY<\/span><br \/>\n<span style=\"color: #000000;\">Consider the 2 triangles, \u2206PQR and \u2206XYZ.<\/span><br \/>\n<span style=\"color: #000000;\">PQ = XY (Radii\u00a0are equal)<\/span><br \/>\n<span style=\"color: #000000;\">PR = XZ (Radii are equal)<\/span><br \/>\n<span style=\"color: #000000;\">QR = YZ (Chords\u00a0are equal)<\/span><br \/>\n<span style=\"color: #000000;\">By\u00a0SSS congruency, \u2206PQR is\u00a0congruent\u00a0to \u2206XYZ.<\/span><br \/>\n<span style=\"color: #000000;\">So, by CPCT (Corresponding parts of congruent triangles), we get \u2220QPR =\u2220YXZ.<\/span><br \/>\n<span style=\"color: #000000;\">Hence, proved that equal chords of congruent circles subtend equal angles at their centers.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.<br \/>\n<\/strong><strong>Answer &#8211; <\/strong>Using equal angles at the centers and the fact that circles are congruent, we prove the statement using Side-Angle-Side (SAS criteria) and corresponding parts of congruent triangles (CPCT).<br \/>\nDraw chords QR and YZ in two\u00a0congruent circles as shown above. Join the radii PR, PQ, and XY, XZ respectively.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-4529\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.2-Ans2.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"378\" height=\"177\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.2-Ans2.png 795w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.2-Ans2-300x140.png 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.2-Ans2-768x359.png 768w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.2-Ans2-480x225.png 480w\" sizes=\"auto, (max-width: 378px) 100vw, 378px\" \/><br \/>\nGiven that chords subtend equal angles at the center. So, \u2220QPR = \u2220YXZ.<\/span><br \/>\n<span style=\"color: #000000;\">We need to prove that chords are equal, that is,\u00a0QR = YZ<\/span><br \/>\n<span style=\"color: #000000;\">Since the circles are\u00a0congruent, their radii will be equal.<\/span><br \/>\n<span style=\"color: #000000;\">PR = PQ = XZ = XY<\/span><br \/>\n<span style=\"color: #000000;\">Consider the two\u00a0triangles \u2206PQR and \u2206XYZ.<\/span><br \/>\n<span style=\"color: #000000;\">PQ = XY (Radii are equal)<\/span><br \/>\n<span style=\"color: #000000;\">\u2220QPR = \u2220YXZ (Chords\u00a0subtend equal angles at center)<\/span><br \/>\n<span style=\"color: #000000;\">PR = XZ (Radii\u00a0are equal)<\/span><br \/>\n<span style=\"color: #000000;\">By SAS criteria, \u2206PQR is congruent to \u2206XYZ.<\/span><br \/>\n<span style=\"color: #000000;\">So,\u00a0QR = YZ\u00a0(Corresponding parts of\u00a0congruent triangles)<\/span><br \/>\n<span style=\"color: #000000;\">Hence proved if chords of congruent circles subtend equal angles at their center then the chords are equal.<\/span><\/p>\n<p style=\"text-align: justify;\">\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 9 Maths\u00a0 Chapter &#8211; 10 (Circles)\u00a0 The NCERT Solutions in English Language for Class 9 Mathematics\u00a0Chapter &#8211; 10 Circles Exercise 10.2 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter 10: Circles NCERT Solution Class 9 Maths Ex &#8211; 10.1 NCERT Solution Class 9 Maths [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[698],"tags":[719,702,186,720,701,5],"class_list":["post-4518","post","type-post","status-publish","format-standard","hentry","category-class-9-maths","tag-class-9th-chapter-10-circles-in-english","tag-ncert-solution-class-9","tag-ncert-solutions","tag-ncert-solutions-class-9-maths-chapter-10-in-english","tag-ncert-solutions-class-9-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.4) - 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