{"id":72161,"date":"2021-02-04T15:20:00","date_gmt":"2021-02-04T09:50:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=72161"},"modified":"2021-02-04T15:20:06","modified_gmt":"2021-02-04T09:50:06","slug":"rd-sharma-chapter-16-class-9-maths-exercise-16-2-solutions","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-16-class-9-maths-exercise-16-2-solutions\/","title":{"rendered":"RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions"},"content":{"rendered":"\n<p>RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions help the students better understand the congruence of circles and the arcs. The entire chapter 16 comprises different topics on Circles explained thoroughly with a stepwise approach.\u00a0<\/p>\n<p>Upon exercising the RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions, the student can get stronger with his\/ her fundamentals about the circle while boosting deep understanding to address problems around the circle. Learners have access to download the PDF that consists of complete explanations and examples, which helps students to score well in the exam.<\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-16-circles\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Learn about RD Sharma Chapter 16 Class 9<\/strong><\/a><\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69db9bdf241e2\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #000000;color:#000000\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-69db9bdf241e2\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-16-class-9-maths-exercise-16-2-solutions\/#download-rd-sharma-chapter-16-class-9-maths-exercise-162-solutions-pdf\" title=\"Download RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions PDF\">Download RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions PDF<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-16-class-9-maths-exercise-16-2-solutions\/#important-definitions-rd-sharma-chapter-16-class-9-maths-exercise-162-solutions\" title=\"Important Definitions RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions\">Important Definitions RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-16-class-9-maths-exercise-16-2-solutions\/#congruence-of-circles-and-arcs\" title=\"Congruence of Circles and Arcs\">Congruence of Circles and Arcs<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-16-class-9-maths-exercise-16-2-solutions\/#congruent-circles\" title=\"Congruent Circles\">Congruent Circles<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-16-class-9-maths-exercise-16-2-solutions\/#congruent-arcs\" title=\"Congruent Arcs\">Congruent Arcs<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-16-class-9-maths-exercise-16-2-solutions\/#some-essentials-results-on-congruent-arcs-and-chords\" title=\"Some Essentials Results on Congruent Arcs and Chords\">Some Essentials Results on Congruent Arcs and Chords<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-16-class-9-maths-exercise-16-2-solutions\/#examples-of-rd-sharma-chapter-16-class-9-maths-exercise-162-solutions\" title=\"Examples of RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions\">Examples of RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-16-class-9-maths-exercise-16-2-solutions\/#benefits-of-rd-sharma-chapter-16-class-9-maths-exercise-162-solutions\" title=\"Benefits of RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions\">Benefits of RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-chapter-16-class-9-maths-exercise-162-solutions-pdf\"><\/span>Download RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 500px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br \/><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/Solutions-for-Class-9-Maths-Chapter-16-Circles-Exercise-16.2.pdf, \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/Solutions-for-Class-9-Maths-Chapter-16-Circles-Exercise-16.2.pdf\">Solutions for Class 9 Maths Chapter 16 Circles Exercise 16.2<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"important-definitions-rd-sharma-chapter-16-class-9-maths-exercise-162-solutions\"><\/span>Important Definitions RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In this RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions, we will discuss the topics and subtopics mentioned in the following points-<\/p>\n<ol>\n<li>Congruence of circles and arcs<\/li>\n<\/ol>\n<ul>\n<li>Congruent circles<\/li>\n<li>Congruent arcs<\/li>\n<\/ul>\n<ol start=\"2\">\n<li>Some essentials result in Congruent arcs and chords<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"congruence-of-circles-and-arcs\"><\/span><strong>Congruence of Circles and Arcs<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Here we will learn about the formal definition of congruence for each shape. Get down to know the complete information.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"congruent-circles\"><\/span><strong>Congruent Circles<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Congruent Circles are circles when two circles have congruent radii.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"congruent-arcs\"><\/span><strong>Congruent Arcs<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Congruent Arcs are the arcs when two arcs are equal in measure and segments of congruent circles.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"some-essentials-results-on-congruent-arcs-and-chords\"><\/span><strong>Some Essentials Results on Congruent Arcs and Chords<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ol>\n<li>A diameter\/ radius is perpendicular to a chord, and then it divides the chord and its arc.<\/li>\n<li>Two chords are congruent, and then their equal arcs are congruent.<\/li>\n<li>A diameter\/ radius is perpendicular to a chord, and then it divides the chord and its arc.<\/li>\n<li>In the congruent circle, two chords are congruent if they are equidistant to the center.<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"examples-of-rd-sharma-chapter-16-class-9-maths-exercise-162-solutions\"><\/span><strong>Examples of RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ques- The radius of a circle is 8 cm, and the length of one of its chords is 12 cm. Get the extent (distance) of the chord from the center.<\/strong><\/p>\n<p><strong>Solution-<\/strong><\/p>\n<ul>\n<li>Radius of circle (OP) = 8 cm (Given)<\/li>\n<li>Chord (PQ) = 12cm (Given)<\/li>\n<\/ul>\n<p>Draw a perpendicular OR on PQ.<\/p>\n<p>We know, perpendicular from center to chord bisects the chord<\/p>\n<p>Which implies, PR = QR = 12\/2 = 6 cm<\/p>\n<p>In right \u0394ORP:<\/p>\n<p>Using Pythagoras theorem,<\/p>\n<p>OP2 = PR2 + OR2<\/p>\n<p>64 = 36 + OR2<\/p>\n<p>OR2 = 64 \u2013 36 = 28<\/p>\n<p>or OR = \u221a28 = 5.291 (approx.)<\/p>\n<p>The extent (distance) of the chord from the center is 5.291 cm.<\/p>\n<p><strong>Ques:<\/strong> Find the length of a chord, which is at an extent (distance) of 5cm from the center of the circle of radius 10cm.<\/p>\n<p>Solution-<\/p>\n<p>Distance of the chord from the centre = OZ = 5 cm (Given)<\/p>\n<p>Radius of the circle = OX = 10 cm (Given)<\/p>\n<p>In \u0394OZX:<\/p>\n<p>Using Pythagoras theorem,<\/p>\n<p>OX2 = XZ2 + OZ2<\/p>\n<p>100 = XZ2 + 25<\/p>\n<p>XZ2 = 100 \u2013 25 = 75<\/p>\n<p>XZ = \u221a75 = 8.66<\/p>\n<p>As, perpendicular from the center to chord bisects the chord.<\/p>\n<p>Therefore, XZ = YZ = 8.66 cm<\/p>\n<p>= XY = XZ + YZ = 8.66 + 8.66 = 17.32<\/p>\n<p>Answer: XY = 17.32 cm<\/p>\n<p><strong>Ques:<\/strong> Find the length of a chord, which is at an extent (distance) of 4cm from the center of the circle of radius 6 cm.<\/p>\n<p>Solution-<\/p>\n<ul>\n<li>Distance of the chord from the center = OR = 4 cm (Given)<\/li>\n<li>Radius of the circle = OP = 6 cm (Given)<\/li>\n<\/ul>\n<p>In \u0394ORP:<\/p>\n<p>Using Pythagoras theorem,<\/p>\n<p>OP2 = PR2 + OR2<\/p>\n<p>36 = PR2 + 16<\/p>\n<p>PR2 = 36 \u2013 16 = 20<\/p>\n<p>PR = \u221a20 = 4.47<\/p>\n<p>Or PR = 4.47cm<\/p>\n<p>As, perpendicular to the centre to chord bisects the chord.<\/p>\n<p>Therefore, PR = QR = 4.47 cm<\/p>\n<p>= PQ = PR + QR = 4.47 + 4.47 = 8.94<\/p>\n<p>Answer- PQ = 8.94 cm<\/p>\n<h3><span class=\"ez-toc-section\" id=\"benefits-of-rd-sharma-chapter-16-class-9-maths-exercise-162-solutions\"><\/span><strong>Benefits of RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>This RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions can be useful for the students in exercising numerous questions revolving around the theories of circles, be it about the radius, sector, segment, and circle diameter. A student can certainly expect a good score upon practicing these questions. Specifically, these solutions can be beneficial for students to practice within a minimum time period before the exam, yet can be hopeful about scoring good marks.<\/p>\n<p><a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener noreferrer\">Know about CBSE Board<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions help the students better understand the congruence of circles and the arcs. The entire chapter 16 comprises different topics on Circles explained thoroughly with a stepwise approach.\u00a0 Upon exercising the RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions, the student can get stronger &#8230; <a title=\"RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-16-class-9-maths-exercise-16-2-solutions\/\" aria-label=\"More on RD Sharma Chapter 16 Class 9 Maths Exercise 16.2 Solutions\">Read more<\/a><\/p>\n","protected":false},"author":241,"featured_media":72163,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2985,2917,73719,73411],"tags":[3081,3086,3085],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/72161"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/241"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=72161"}],"version-history":[{"count":3,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/72161\/revisions"}],"predecessor-version":[{"id":73421,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/72161\/revisions\/73421"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/72163"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=72161"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=72161"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=72161"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}