{"id":72311,"date":"2021-02-04T15:20:05","date_gmt":"2021-02-04T09:50:05","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=72311"},"modified":"2021-02-04T15:20:12","modified_gmt":"2021-02-04T09:50:12","slug":"rd-sharma-chapter-16-class-9-maths-exercise-16-4-solutions","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-16-class-9-maths-exercise-16-4-solutions\/","title":{"rendered":"RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 Solutions"},"content":{"rendered":"\n<p>RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 Solutions is one of the prime sections of the chapter called \u2018Circle.\u2019 Upon exercising the questions in these sections, the students can get in-depth knowledge about arcs formed upon these. The key to answering the questions based on these problems is always about following the steps right. Rather than traditional ways, a step-by-step method of answering the questions on it is a better approach. Otherwise, it might look complicated. Also, step by answering the questions can help a student have a better knowledge of the topic.<\/p>\n<p>Students will get the varieties of questions in the attached PDF based on the RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 Solutions. The explanation given in the PDF is prepared with easy solutions as per the learners\u2019 understanding. All the formulas are mentioned with the proof along with the questions.<\/p>\n<p><a href=\"_wp_link_placeholder\" data-wplink-edit=\"true\"><strong>Learn about RD Sharma Chapter 16 Circles 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-69dbb01b63caf\" 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-69dbb01b63caf\"><\/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-16-4-solutions\/#download-rd-sharma-chapter-16-class-9-maths-exercise-164-solutions-pdf\" title=\"Download RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 Solutions PDF\">Download RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 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-16-4-solutions\/#important-definitions-rd-sharma-chapter-16-class-9-maths-exercise-164-solutions\" title=\"Important Definitions RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 Solutions\">Important Definitions RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 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-16-4-solutions\/#examples-of-arcs-and-its-subtented-angles-of-rd-sharma-chapter-16-class-9-maths-exercise-164-solutions\" title=\"Examples of Arcs and Its Subtented Angles of RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 Solutions\">Examples of Arcs and Its Subtented Angles of RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 Solutions<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-16-class-9-maths-exercise-16-4-solutions\/#frequently-asked-questions-faqs-of-rd-sharma-chapter-16-class-9-maths-exercise-164-solutions\" title=\"Frequently Asked Questions (FAQs) of RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 Solutions\">Frequently Asked Questions (FAQs) of RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 Solutions<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-chapter-16-class-9-maths-exercise-164-solutions-pdf\"><\/span>Download RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 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-16.4.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-16.4.pdf\">Solutions for Class 9 Maths Chapter 16 Circles Exercise 16.4<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"important-definitions-rd-sharma-chapter-16-class-9-maths-exercise-164-solutions\"><\/span>Important Definitions RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>An angle subtended by the arc of a circle at its center is twice (two times) the angle it subtends anyplace on the circle&#8217;s circumference.<\/p>\n<p>To prove the arcs and their subtended angles, we have to take the exterior angle theorem, where an exterior angle of a triangle is equivalent to the total of the opposite interior angles.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"examples-of-arcs-and-its-subtented-angles-of-rd-sharma-chapter-16-class-9-maths-exercise-164-solutions\"><\/span>Examples of Arcs and Its Subtented Angles of RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 Solutions<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ques- In the below figure, O is the center of a circle. If \u2220APB = 50\u00b0, find \u2220AOB and \u2220OAB.<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-72312 aligncenter\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/fig-8.png\" alt=\"RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 Solutions\" width=\"264\" height=\"271\" \/><\/p>\n<p><strong>Solution-<\/strong><\/p>\n<p>= \u2220APB = 50\u00b0 (Given)<\/p>\n<p>= By degree measure theorem: \u2220AOB = 2\u2220APB<\/p>\n<p>= \u2220AOB = 2 \u00d7 50\u00b0 = 100\u00b0<\/p>\n<p>= Again, OA = OB [Radius of circle]<\/p>\n<p>= Then \u2220OAB = \u2220OBA [Angles opposite to equal sides]<\/p>\n<p>= Let \u2220OAB = m<\/p>\n<p>= In \u0394OAB,<\/p>\n<p>= By an angle sum property: \u2220OAB+\u2220OBA+\u2220AOB=1800<\/p>\n<p>= m + m + 100\u00b0 = 180\u00b0<\/p>\n<p>= 2m = 180\u00b0 \u2013 100\u00b0 = 80\u00b0<\/p>\n<p>= m = 80\u00b0\/2 = 40\u00b0<\/p>\n<p>=\u2220OAB = \u2220OBA = 40\u00b0<\/p>\n<p><strong>Que- In the below figure, it is given that O is the centre of a circle and \u2220AOC = 150\u00b0. Find \u2220ABC.<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-72435\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/fig-9.png\" alt=\"RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 Solutions\" width=\"750\" height=\"538\" \/><\/p>\n<p><strong>Solution-<\/strong><\/p>\n<p>= \u2220AOC = 150\u00b0 (Given)<\/p>\n<p>= By degree measure theorem-<\/p>\n<p>= \u2220ABC = (reflex \u2220AOC)\/2 \u2026(1)<\/p>\n<p>= We know, \u2220AOC + reflex(\u2220AOC) = 360\u00b0 [Complex angle]<\/p>\n<p>= 150\u00b0 + reflex \u2220AOC = 360\u00b0<\/p>\n<p>= or reflex \u2220AOC = 360\u00b0\u2212150\u00b0 = 210\u00b0<\/p>\n<p>=From (1) =&gt; \u2220ABC = 210\u00b0 \/2 = 105\u00b0<\/p>\n<p><strong>Ques- In the following figure, O is the centre of a circle. Find \u2220BAC.<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-72436\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/fig-10.png\" alt=\"RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 Solutions\" width=\"750\" height=\"538\" \/><\/p>\n<p><strong>Solution-<\/strong><\/p>\n<p>Given: \u2220AOB = 80\u00b0 and \u2220AOC = 110\u00b0<\/p>\n<p>= Therefore, \u2220AOB+ \u2220AOC+ \u2220BOC=360\u00b0 [Completeangle]<\/p>\n<p>= Substitute of given values,<\/p>\n<p>= 80\u00b00 + 100\u00b0 + \u2220BOC = 360\u00b0<\/p>\n<p>= \u2220BOC = 360\u00b0 \u2013 80\u00b0 \u2013 110\u00b0 = 170\u00b0<\/p>\n<p>= or \u2220BOC = 170\u00b0<\/p>\n<p>= Now, by degree measure theorem<\/p>\n<p>= \u2220BOC = 2\u2220BAC<\/p>\n<p>= 170\u00b0 = 2\u2220BAC<\/p>\n<p>= Or \u2220BAC = 170\u00b0\/2 = 85\u00b0<\/p>\n<h2><span class=\"ez-toc-section\" id=\"frequently-asked-questions-faqs-of-rd-sharma-chapter-16-class-9-maths-exercise-164-solutions\"><\/span>Frequently Asked Questions (FAQs) of RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Ques 1- What is the angle subtended by an arc?<\/p>\n<p>Ans- An angle is subtended by an arc, line segment, or some other section of a curve when its two rays cross through the endpoints of the arc, line segment, or curve section.<\/p>\n<p>Ques 2- What is a subtended angle at the circumference?<\/p>\n<p>Ans- If the endpoints of an arc are connected to a third point on the circumference of the circle, then an angle is created.<\/p>\n<p>Ques 3- How do you find the length of an arc without an angle?<\/p>\n<p>Ans- To measure arc length without an angle, we need the radius and the sector area (Multiply the area by 2). Then divide the outcome by the radius squared (ensure that the units are equal) to make the central angle in radians.<\/p>\n<p><a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Know about CBSE Board<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 Solutions is one of the prime sections of the chapter called \u2018Circle.\u2019 Upon exercising the questions in these sections, the students can get in-depth knowledge about arcs formed upon these. The key to answering the questions based on these problems is always about following the steps &#8230; <a title=\"RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 Solutions\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-16-class-9-maths-exercise-16-4-solutions\/\" aria-label=\"More on RD Sharma Chapter 16 Class 9 Maths Exercise 16.4 Solutions\">Read more<\/a><\/p>\n","protected":false},"author":241,"featured_media":72434,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2917,73719,73411,2985],"tags":[3081,3086,3085],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/72311"}],"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=72311"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/72311\/revisions"}],"predecessor-version":[{"id":73423,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/72311\/revisions\/73423"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/72434"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=72311"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=72311"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=72311"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}