{"id":5435,"date":"2026-07-08T11:23:58","date_gmt":"2026-07-08T05:53:58","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=5435"},"modified":"2026-07-08T11:24:08","modified_gmt":"2026-07-08T05:54:08","slug":"ncert-class-9-maths-chapter-5-end-of-chapter-exercise-solutions","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/ncert-class-9-maths-chapter-5-end-of-chapter-exercise-solutions\/","title":{"rendered":"NCERT Class 9 Maths Chapter 5 End-of-Chapter Exercise Solutions"},"content":{"rendered":"<div class=\"mymoc-top mymoc-entity-placement\" id=\"mymoc-3619604043\"><div id=\"mymoc-4190942388\"><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\/5435?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\">5<\/span><\/div>\n<h1 class=\"wp-block-heading\">Short Introduction<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">The End-of-Chapter Exercise of Chapter 5, <em>I&rsquo;m Up and Down, and Round and Round<\/em>, helps students revise all important concepts related to circles. This exercise covers:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Properties of chords<\/li>\n\n\n\n<li>Circumcircle and circumcentre<\/li>\n\n\n\n<li>Distance of chords from the centre<\/li>\n\n\n\n<li>Angles subtended by arcs<\/li>\n\n\n\n<li>Diameter theorem<\/li>\n\n\n\n<li>Concyclic points<\/li>\n\n\n\n<li>Applications of circle theorems<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">This chapter forms an important foundation for higher geometry in Classes 10 and 11.<\/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>End-of-Chapter Exercise<\/td><\/tr><tr><td>Main Topic<\/td><td>Circle Theorems and Applications<\/td><\/tr><tr><td>Difficulty Level<\/td><td>Moderate<\/td><\/tr><tr><td>Important Topics<\/td><td>Chords, Angles, Circumcircle, Concyclicity<\/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<p class=\"wp-block-paragraph\">&#10004; Definition of Circle<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10004; Radius, Chord and Diameter<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10004; Circumcentre and Circumcircle<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10004; Equal Chords and Equal Angles<\/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\">NCERT Class 9 Maths Exercise 1.1 Solutions | Coordinate Geometry NCERT Solutions<\/span><\/a><\/div><p class=\"wp-block-paragraph\">&#10004; Perpendicular Bisector of Chords<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10004; Distance of Chords from Centre<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10004; Angles in the Same Segment<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10004; Diameter Theorem<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10004; Concyclic Points<\/p>\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 Theorems<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">1. Radius Property<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"819\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-29-1024x819.png\" alt=\"\" class=\"wp-image-6253\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-29-1024x819.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-29-300x240.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-29-768x615.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-29-640x512.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-29.png 1402w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">2. Chord Length Formula<\/h2>\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\/07\/image-31-819x1024.png\" alt=\"\" class=\"wp-image-6255\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-31-819x1024.png 819w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-31-240x300.png 240w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-31-768x960.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-31-640x800.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-31.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<h2 class=\"wp-block-heading\">3. Angle Theorem<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"909\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-32-909x1024.png\" alt=\"\" class=\"wp-image-6257\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-32-909x1024.png 909w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-32-266x300.png 266w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-32-768x866.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-32-640x721.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-32.png 1181w\" sizes=\"(max-width: 909px) 100vw, 909px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">4. Diameter Theorem<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"933\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-33-933x1024.png\" alt=\"\" class=\"wp-image-6259\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-33-933x1024.png 933w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-33-273x300.png 273w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-33-768x843.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-33-640x703.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-33.png 1197w\" sizes=\"(max-width: 933px) 100vw, 933px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">5. Equal Chords Theorem<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"859\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-34-859x1024.png\" alt=\"\" class=\"wp-image-6261\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-34-859x1024.png 859w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-34-252x300.png 252w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-34-768x915.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-34-640x763.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-34.png 1149w\" sizes=\"(max-width: 859px) 100vw, 859px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">6. Converse<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"859\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-35-859x1024.png\" alt=\"\" class=\"wp-image-6263\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-35-859x1024.png 859w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-35-252x300.png 252w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-35-768x915.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-35-640x763.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-35.png 1149w\" sizes=\"(max-width: 859px) 100vw, 859px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">End-of-Chapter Exercise Solutions<\/h1>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 1<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>In a circle, a chord is 5 cm away from the centre. If the radius of the circle is 13 cm, what is the length of the chord?<\/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 loading=\"lazy\" decoding=\"async\" width=\"859\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-36-859x1024.png\" alt=\"\" class=\"wp-image-6264\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-36-859x1024.png 859w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-36-252x300.png 252w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-36-768x915.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-36-640x763.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-36.png 1149w\" sizes=\"(max-width: 859px) 100vw, 859px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 2<\/h1>\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=\"has-medium-font-size wp-block-paragraph\"><strong>An arc of a circle subtends an angle of 70&deg; at the centre. What is the measure of the angle subtended by the arc at a point on the circle?<\/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 loading=\"lazy\" decoding=\"async\" width=\"859\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-37-859x1024.png\" alt=\"\" class=\"wp-image-6266\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-37-859x1024.png 859w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-37-252x300.png 252w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-37-768x915.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-37-640x763.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-37.png 1149w\" sizes=\"(max-width: 859px) 100vw, 859px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 3<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>The diameter of a circle is 26 cm. A chord of length 24 cm is drawn in the circle. Find the distance from the centre of the circle to the chord.<\/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 loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-38-1024x683.png\" alt=\"\" class=\"wp-image-6277\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-38-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-38-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-38-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-38-640x427.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-38-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-38.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 4<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>A circle has a radius of 15 cm. A chord is drawn. The distance from the centre of the circle to the chord is 9 cm. What is the length of the chord?<\/strong><\/p><div class=\"mymoc-middle mymoc-entity-placement\" id=\"mymoc-133493301\"><div id=\"mymoc-1834603594\"><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>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-39-1024x683.png\" alt=\"\" class=\"wp-image-6280\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-39-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-39-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-39-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-39-640x427.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-39-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-39.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 5<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Prove that the perpendicular bisector of a chord passes through the centre of the circle.<\/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 loading=\"lazy\" decoding=\"async\" width=\"683\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-40-683x1024.png\" alt=\"\" class=\"wp-image-6282\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-40-683x1024.png 683w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-40-200x300.png 200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-40-768x1152.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-40-640x960.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-40-600x900.png 600w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-40.png 1024w\" sizes=\"(max-width: 683px) 100vw, 683px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 6<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>The diameter of a circle is AB. Point C is on the circumference. What is the measure of the &ang;ACB? Explain your reasoning.<\/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 loading=\"lazy\" decoding=\"async\" width=\"683\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-41-683x1024.png\" alt=\"\" class=\"wp-image-6284\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-41-683x1024.png 683w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-41-200x300.png 200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-41-768x1152.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-41-640x960.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-41-600x900.png 600w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-41.png 1024w\" sizes=\"(max-width: 683px) 100vw, 683px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 7<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>ABCD is a cyclic quadrilateral inscribed in a circle. If &ang;A measures 75&deg;, what is the measure of &ang;C? If &ang;B measures 110&deg;, what is the measure of &ang;D?<\/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 loading=\"lazy\" decoding=\"async\" width=\"887\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-42-887x1024.png\" alt=\"\" class=\"wp-image-6285\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-42-887x1024.png 887w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-42-260x300.png 260w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-42-768x886.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-42-640x739.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-42.png 1167w\" sizes=\"(max-width: 887px) 100vw, 887px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 8<\/h1>\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=\"has-medium-font-size wp-block-paragraph\"><strong>Quadrilateral PQRS is inscribed in a circle. If &ang;P = (2x + 10)&deg; and &ang;R = (3x &minus; 20)&deg;, find the value of x and the measures of &ang;P and &ang;R.<\/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 loading=\"lazy\" decoding=\"async\" width=\"683\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-43-683x1024.png\" alt=\"\" class=\"wp-image-6289\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-43-683x1024.png 683w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-43-200x300.png 200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-43-768x1152.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-43-640x960.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-43-600x900.png 600w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-43.png 1024w\" sizes=\"(max-width: 683px) 100vw, 683px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 9<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>The distance of a chord of length 16 cm from the centre of a circle is 6 cm. Find the radius of the circle.<\/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 loading=\"lazy\" decoding=\"async\" width=\"819\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-44-819x1024.png\" alt=\"\" class=\"wp-image-6290\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-44-819x1024.png 819w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-44-240x300.png 240w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-44-768x960.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-44-640x800.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-44.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\">Question 10<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>What aA cyclic quadrilateral has sides 5, 5, 12, 12 units. Find its area.re concyclic points?<\/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 loading=\"lazy\" decoding=\"async\" width=\"683\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-45-683x1024.png\" alt=\"\" class=\"wp-image-6292\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-45-683x1024.png 683w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-45-200x300.png 200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-45-768x1152.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-45-640x960.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-45-600x900.png 600w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-45.png 1024w\" sizes=\"(max-width: 683px) 100vw, 683px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 11<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Consider a cyclic quadrilateral. Without drawing its circumcircle, how can we find out whether the centre of the circumcircle lies inside the quadrilateral or outside? What is the best way of finding out?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"683\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-46-683x1024.png\" alt=\"\" class=\"wp-image-6295\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-46-683x1024.png 683w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-46-200x300.png 200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-46-768x1152.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-46-640x960.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-46-600x900.png 600w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-46.png 1024w\" sizes=\"(max-width: 683px) 100vw, 683px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 12<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>When two chords intersect, each of them is divided into two line segments. Show that if the intersecting chords are of equal length, then the line segments of one chord are equal to the<br>corresponding line segments of the other chord.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"859\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-47-859x1024.png\" alt=\"\" class=\"wp-image-6297\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-47-859x1024.png 859w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-47-252x300.png 252w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-47-768x915.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-47-640x763.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-47.png 1149w\" sizes=\"(max-width: 859px) 100vw, 859px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 13<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Draw a circle in which a chord of 6 cm length stands at a distance of 3 cm from the centre.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"859\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-48-859x1024.png\" alt=\"\" class=\"wp-image-6301\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-48-859x1024.png 859w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-48-252x300.png 252w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-48-768x915.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-48-640x763.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-48.png 1149w\" sizes=\"(max-width: 859px) 100vw, 859px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 14<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Show that rectangle is the only parallelogram that can be inscribed in a circle.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"859\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-49-859x1024.png\" alt=\"\" class=\"wp-image-6303\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-49-859x1024.png 859w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-49-252x300.png 252w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-49-768x915.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-49-640x763.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-49.png 1149w\" sizes=\"(max-width: 859px) 100vw, 859px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 15<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Show that if a rectangle is inscribed in a circle, then the point of intersection of its diagonals must lie at the centre of the circle.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"859\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-50-859x1024.png\" alt=\"\" class=\"wp-image-6304\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-50-859x1024.png 859w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-50-252x300.png 252w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-50-768x915.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-50-640x763.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-50.png 1149w\" sizes=\"(max-width: 859px) 100vw, 859px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 16<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Consider all chords of a circle of a fixed length. What is the shape formed by the midpoints of all these chords?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"859\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-51-859x1024.png\" alt=\"\" class=\"wp-image-6307\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-51-859x1024.png 859w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-51-252x300.png 252w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-51-768x915.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-51-640x763.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-51.png 1149w\" sizes=\"(max-width: 859px) 100vw, 859px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 17<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>In a circle with centre O, chords AB and AC are congruent. Explain why this statement is true: &ldquo;The centre of the circle lies on the angle bisector of &ang;BAC&rdquo;.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"859\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-52-859x1024.png\" alt=\"\" class=\"wp-image-6311\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-52-859x1024.png 859w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-52-252x300.png 252w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-52-768x915.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-52-640x763.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-52.png 1149w\" sizes=\"(max-width: 859px) 100vw, 859px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 18<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Two parallel chords of lengths 10 cm and 24 cm are on the same side of the centre of a circle. The distance between the chords is 7 cm. Find the radius of the circle.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"859\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-53-859x1024.png\" alt=\"\" class=\"wp-image-6312\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-53-859x1024.png 859w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-53-252x300.png 252w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-53-768x915.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-53-640x763.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-53.png 1149w\" sizes=\"(max-width: 859px) 100vw, 859px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 19<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>A regular hexagon is inscribed in a circle of radius r. Find the length of the sides of the hexagon and the distance of each side from the centre of the circle.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"859\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-54-859x1024.png\" alt=\"\" class=\"wp-image-6314\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-54-859x1024.png 859w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-54-252x300.png 252w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-54-768x915.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-54-640x763.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-54.png 1149w\" sizes=\"(max-width: 859px) 100vw, 859px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 20<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>A quadrilateral MNOP is inscribed in a circle. If MN is a diameter, what can you say about &ang;MOP and &ang;MNP? Explain your reasoning.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"928\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-59-928x1024.png\" alt=\"\" class=\"wp-image-6322\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-59-928x1024.png 928w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-59-272x300.png 272w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-59-768x847.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-59-640x706.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-59.png 1194w\" sizes=\"(max-width: 928px) 100vw, 928px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 21<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Let ABCD be a cyclic quadrilateral. Explain why the exterior angle at any vertex is equal to the interior opposite angle (e.g., &ang;CDE = &ang;ABC, where E is a point on the extension of side CD).<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-55-1024x683.png\" alt=\"\" class=\"wp-image-6316\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-55-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-55-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-55-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-55-640x427.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-55-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-55.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 22<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>There is no chord of a circle that is longer than its diameter.&rdquo; How do you justify this statement?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-58-1024x683.png\" alt=\"\" class=\"wp-image-6321\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-58-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-58-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-58-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-58-640x427.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-58-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-58.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 23<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Let A be any point within a given circle with centre O. Show that the shortest chord of the circle that passes through point A is the one that is perpendicular to OA.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"906\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-57-906x1024.png\" alt=\"\" class=\"wp-image-6320\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-57-906x1024.png 906w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-57-266x300.png 266w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-57-768x868.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-57-640x723.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-57.png 1180w\" sizes=\"(max-width: 906px) 100vw, 906px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 24<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>How would you use the following figure to justify the statement that the angle in a semicircle is 90&deg;?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"819\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-60-1024x819.png\" alt=\"\" class=\"wp-image-6324\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-60-1024x819.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-60-300x240.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-60-768x615.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-60-640x512.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-60.png 1402w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 25<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>In a circle, two chords CC&rsquo; and DD&rsquo; are drawn perpendicular to a diameter AB. Prove that the segment MM&rsquo; joining the midpoints of the chords CD and C&rsquo; D&rsquo; is perpendicular to AB.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"960\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-61-960x1024.png\" alt=\"\" class=\"wp-image-6327\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-61-960x1024.png 960w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-61-281x300.png 281w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-61-768x819.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-61-640x683.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-61.png 1214w\" sizes=\"(max-width: 960px) 100vw, 960px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 26<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>How would you use the following figure to justify the statement that the sum of the opposite angles of a cyclic quadrilateral is 180&deg;?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-62-852x1024.png\" alt=\"\" class=\"wp-image-6331\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-62-852x1024.png 852w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-62-250x300.png 250w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-62-768x923.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-62-640x769.png 640w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/07\/image-62.png 1144w\" sizes=\"(max-width: 852px) 100vw, 852px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Final Revision Notes<\/h1>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Theorem<\/th><th>Result<\/th><\/tr><\/thead><tbody><tr><td>Theorem 1<\/td><td>Unique circle through three non-collinear points<\/td><\/tr><tr><td>Theorem 2<\/td><td>Equal chords subtend equal angles<\/td><\/tr><tr><td>Theorem 3<\/td><td>Equal central angles have equal chords<\/td><\/tr><tr><td>Theorem 4<\/td><td>Line joining centre to midpoint of chord is perpendicular<\/td><\/tr><tr><td>Theorem 5<\/td><td>Perpendicular from centre bisects chord<\/td><\/tr><tr><td>Theorem 6<\/td><td>Equal chords are equidistant from centre<\/td><\/tr><tr><td>Theorem 7<\/td><td>Equidistant chords are equal<\/td><\/tr><tr><td>Theorem 8<\/td><td>Longer chord lies nearer the centre<\/td><\/tr><tr><td>Theorem 9<\/td><td>Angle at centre = 2 &times; angle at circumference<\/td><\/tr><tr><td>Corollary<\/td><td>Diameter subtends a right angle<\/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\">Common Mistakes<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">&#10060; Forgetting that the angle at the centre is twice the angle at the circumference.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10060; Confusing chord and diameter.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10060; Using full chord instead of half-chord in calculations.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10060; Assuming all equal angles lie on the same side of a chord.<\/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; Learn all theorems in sequence.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10004; Draw neat labelled diagrams.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10004; Remember:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diameter = Longest chord.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10004; Practice proof-based questions regularly.<\/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 longest chord of a circle is:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. Radius<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. Diameter<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. Arc<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. Tangent<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answer:<\/strong> B<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">2. Equal chords are:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. Parallel<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. Equidistant from the centre<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. Perpendicular<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. Diameters<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answer:<\/strong> B<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">3. Angle subtended by a diameter is:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. 45&deg;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. 90&deg;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. 180&deg;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. 60&deg;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answer:<\/strong> B<\/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 an angle at the circumference is 30&deg;, then the angle at the centre is:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. 15&deg;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. 30&deg;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. 45&deg;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. 60&deg;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answer:<\/strong> D<\/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. Can three collinear points lie on a circle?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">No.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">Q2. Which is the greatest chord?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Diameter.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">Q3. What are concyclic points?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Points lying on the same circle.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">Q4. Why are equal chords important?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Because they help determine equal distances and equal central angles.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">Q5. Which theorem is most important in this chapter?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Angle at Centre = 2 &times; Angle at Circumference.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Chapter Summary<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; Circle is the set of points equidistant from a fixed point.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; Diameter is the greatest chord.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; Equal chords are equidistant from the centre.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; Longer chords lie nearer the centre.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; Angles in the same segment are equal.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; Diameter subtends a right angle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; Concyclic points lie on the same circle.<\/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 complete NCERT Solutions and Exam Notes?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Visit <strong><a href=\"http:\/\/www.mymockmate.com\/\">www.mymockmate.com<\/a><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; Complete NCERT Solutions<br>&#9989; Step-by-Step Explanations<br>&#9989; Practice MCQs and Worksheets<br>&#9989; Important Questions and Notes<br>&#9989; Chapter-wise Study Material for Class 9 Maths<\/p>\n<div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/5435?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\">5<\/span><\/div><div class=\"mymoc-bottom mymoc-entity-placement\" id=\"mymoc-4151593405\"><div id=\"mymoc-208663018\"><a href=\"https:\/\/amzn.to\/4ehJfM4\" aria-label=\"students acessories\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/students-acessories.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/students-acessories.png 1301w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/students-acessories-300x85.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/students-acessories-1024x290.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/students-acessories-768x218.png 768w\" sizes=\"(max-width: 1301px) 100vw, 1301px\" width=\"1080\" height=\"100\"><\/a><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p> 5 Short Introduction The End-of-Chapter Exercise of Chapter 5, I&rsquo;m Up and Down, and Round and Round, helps students revise all important concepts related&#8230;<\/p>\n","protected":false},"author":1,"featured_media":5436,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"footnotes":""},"categories":[4,11],"tags":[],"class_list":["post-5435","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-9","category-maths-class-9"],"featured_image_src":"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/NCERT-Class-9-Maths-Chapter-5-End-of-Chapter-Exercise-Solutions.png","author_info":{"display_name":"Team Mymockmate","author_link":"https:\/\/mymockmate.com\/notes\/author\/bsm_adm\/"},"_links":{"self":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/5435","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=5435"}],"version-history":[{"count":39,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/5435\/revisions"}],"predecessor-version":[{"id":6332,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/5435\/revisions\/6332"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/5436"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=5435"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=5435"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=5435"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}