{"id":127983,"date":"2021-09-15T15:52:35","date_gmt":"2021-09-15T10:22:35","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=127983"},"modified":"2021-09-15T15:52:38","modified_gmt":"2021-09-15T10:22:38","slug":"rd-sharma-class-10-solutions-chapter-11-exercise-11-3","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-11-exercise-11-3\/","title":{"rendered":"RD Sharma Class 10 Solutions Chapter 11 Constructions Exercise 11.3 (Updated for 2021-22)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-127995\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-11-Exercise-11.3.jpg\" alt=\"RD Sharma Class 10 Solutions Chapter 11 Exercise 11.3\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-11-Exercise-11.3.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-11-Exercise-11.3-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Class 10 Solutions Chapter 11 Exercise 11.3:\u00a0<\/strong>The construction of tangents to a circle is the key topic covered in this exercise. Students can learn the proper procedures for dealing with difficult problems by approaching <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-for-maths\/\"><strong>RD Sharma Class 10 Solutions<\/strong><\/a>. The <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-11-constructions\/\"><strong>RD Sharma Solutions for Class 10 Maths Chapter 11 Constructions<\/strong><\/a> Exercise 11.3 PDF is given for students below to help them understand how to answer the problems in this exercise.<\/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-69da26a89606d\" 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\" 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href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-11-exercise-11-3\/#download-rd-sharma-class-10-solutions-chapter-11-exercise-113-free-pdf\" title=\"Download RD Sharma Class 10 Solutions Chapter 11 Exercise 11.3 Free PDF\">Download RD Sharma Class 10 Solutions Chapter 11 Exercise 11.3 Free PDF<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-11-exercise-11-3\/#access-answers-to-rd-sharma-solutions-class-10-maths-chapter-11-exercise-113-important-question-with-answers\" title=\"Access answers to RD Sharma Solutions Class 10 Maths Chapter 11 Exercise 11.3- Important Question with Answers\">Access answers to RD Sharma Solutions Class 10 Maths Chapter 11 Exercise 11.3- Important Question with Answers<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" 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href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-11-exercise-11-3\/#does-rd-sharma-solutions-for-class-10-maths-chapter-11-exercise-113-help-you-to-clear-board-exams\" title=\"Does RD Sharma Solutions for Class 10 Maths Chapter 11 Exercise 11.3 help you to clear board exams?\">Does RD Sharma Solutions for Class 10 Maths Chapter 11 Exercise 11.3 help you to clear board exams?<\/a><\/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-class-10-solutions-chapter-11-exercise-11-3\/#where-can-i-get-rd-sharma-class-10-solutions-chapter-11-exercise-113-free-pdf\" title=\"Where can I get RD Sharma Class 10 Solutions Chapter 11 Exercise 11.3 Free PDF?\">Where can I get RD Sharma Class 10 Solutions Chapter 11 Exercise 11.3 Free PDF?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-class-10-solutions-chapter-11-exercise-113-free-pdf\"><\/span>Download RD Sharma Class 10 Solutions Chapter 11 Exercise 11.3 Free 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: 800px;}<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\/09\/RD-Sharma-Solution-Class-10-Chapter-11-Exercise-11.3.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Solution-Class-10-Chapter-11-Exercise-11.3.pdf\">RD Sharma Class 10 Solutions Chapter 11 Exercise 11.3<\/a><\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-answers-to-rd-sharma-solutions-class-10-maths-chapter-11-exercise-113-important-question-with-answers\"><\/span>Access answers to RD Sharma Solutions Class 10 Maths Chapter 11 Exercise 11.3- Important Question with Answers<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Question 1.<br \/>Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.<br \/>Solution:<br \/>Steps of construction :<br \/>(i) Draw a circle with an O centre and 6 cm radius.<br \/>(ii) Take a point P, 10 cm away from the centre O.<br \/>(iii) Join PO and bisect it at M.<br \/>(iv) With centre M and diameter PO, draw a circle intersecting the given circle at T and S.<br \/>(v) Join PT and PS.<br \/>Then PT and PS are the required tangents.<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1944\/44922311374_71da7028c5_o.png\" alt=\"Constructions Class 10 RD Sharma \" width=\"298\" height=\"249\" \/><\/p>\n<p>Question 2.<br \/>Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameters each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.<br \/>Solution:<br \/>Steps of construction :<br \/>(i) Draw a circle with centre O and radius 3 cm.<br \/>(ii) Draw a diameter and produce it to both sides.<br \/>(iii) Take two points P and Q on this diameter with a distance of 7 cm each from the centre O.<br \/>(iv) Bisect PO at M and QO at N<br \/>(v) With centres M and N, draw a circle on PO and QO as diameter which intersects the given circle at S, T, and S\u2019, T\u2019 respectively.<br \/>(vi) Join PS, PT, QS\u2019 and QT\u2019.<br \/>Then PS, PT, QS\u2019 and QT\u2019 are the required tangents to the given circle.<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1918\/45647274851_02ba20c5a3_o.png\" alt=\"RD Sharma Class 10 Solutions Constructions \" width=\"422\" height=\"215\" \/><\/p>\n<p>Question 3.<br \/>Draw a line segment AB of length 8 cm. Taking A as the centre, draw a circle of radius 4 cm, and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle. [CBSE 2013]<br \/>Solution:<br \/>Steps of construction :<br \/>(i) Draw a line segment AB = 8 cm.<br \/>(ii) With centre A and radius 4 cm and with centre B and radius 3 cm, circles are drawn.<br \/>(iii) Bisect AB at M.<br \/>(iv) With centre M and diameter AB, draw a circle that intersects the two circles at S\u2019, T\u2019 and S, T respectively.<br \/>(v) Join AS, AT, BS\u2019and BT\u2019.<br \/>Then AS, AT, BS\u2019 and BT\u2019 are the required tangent.<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1966\/45596779662_d6b0eed2ce_o.png\" alt=\"RD Sharma Class 10 Solutions Constructions Exercise 11.3\" width=\"440\" height=\"266\" \/><\/p>\n<p>Question 4.<br \/>Draw two tangents to a circle of radius 3.5 cm from a point P at a distance of 6.2 cm from its centre.<br \/>Solution:<br \/>Steps of construction :<br \/>(i) Draw a circle with centre O and radius 3.5 cm<br \/>(ii) Take a point P which is 6.2 cm from O.<br \/>(iii) Bisect PO at M and draw a circle with centre M and diameter OP which intersects the given circle at T and S respectively.<br \/>(iv) Join PT and PS.<br \/>PT and PS are the required tangents to circle.<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1926\/45647274751_1944d6f53a_o.png\" alt=\"RD Sharma Class 10 Solutions Chapter 11 Constructions \" width=\"269\" height=\"215\" \/><\/p>\n<p>Question 5.<br \/>Draw a pair of tangents to a circle of radius 4.5 cm, which are inclined to each other at an angle of 45\u00b0. [CBSE 2013]<br \/>Solution:<br \/>Steps of construction :<br \/>The angle at the centre 180\u00b0 \u2013 45\u00b0 = 135\u00b0<br \/>(i) Draw a circle with centre O and radius 4.5 cm.<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1923\/45596779522_5f590f6cac_o.png\" alt=\"RD Sharma Class 10 Pdf Chapter 11 Constructions \" width=\"300\" height=\"190\" \/><br \/>(ii) At O, draw an angle \u2220TOS = 135\u00b0<br \/>(iii) At T and S draw perpendicular which meet each other at P.<br \/>PT and PS are the tangents that inclined each other 45\u00b0.<\/p>\n<p>Question 6.<br \/>Draw a right triangle ABC in which AB = 6 cm, BC = 8 cm and \u2220B = 90\u00b0. Draw BD perpendicular from B on AC and draw a circle passing through the points B, C and D. Construct tangents from A to this circle.<br \/>Solution:<br \/>Steps of Construction :<br \/>Draw a line segment BC = 8 cm<br \/>From B draw an angle of 90\u00b0<br \/>Draw an arc\u00a0BA\u02d8 = 6cm cutting the angle at A.<br \/>Join AC.<br \/>\u0394ABC is the required A.<br \/>Draw \u22a5 bisector of BC cutting BC at M.<br \/>Take M as centre and BM as radius, draw a circle.<br \/>Take A as centre and AB as radius draw an arc cutting the circle at E. Join AE.<br \/>AB and AE are the required tangents.<br \/>Justification :<br \/>\u2220ABC = 90\u00b0 (Given)<br \/>Since OB is a radius of the circle.<br \/>\u2234 AB is a tangent to the circle.<br \/>Also, AE is a tangent to the circle.<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1954\/45647274701_285da77487_o.png\" alt=\"RD Sharma Solutions Class 10 Chapter 11 Constructions \" width=\"247\" height=\"312\" \/><\/p>\n<p>Question 7.<br \/>Draw two concentric circles of radii 3 cm and 5 cm. Construct a tangent to the smaller circle from a point on the larger circle. Also, measure its length. [CBSE 2016]<br \/>Solution:<br \/>Given, two concentric circles of radii 3 cm and 5 cm with centre O. We have to draw pair of tangents from point P on the outer circle to the other.<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1925\/45596779342_12355a25ea_o.png\" alt=\"Learncbse.In Class 10 Chapter 11 Constructions \" width=\"247\" height=\"207\" \/><br \/>Steps of construction :<br \/>(i) Draw two concentric circles with centre O and radii 3 cm and 5 cm.<br \/>(ii) Taking any point P on the outer circle. Join OP.<br \/>(iii) Bisect OP, let M\u2019 be the mid-point of OP.<br \/>Taking M\u2019 as centre and OM\u2019 as radius draw a circle dotted which cuts the inner circle as M and P\u2019.<br \/>(iv) Join PM and PP\u2019. Thus, PM and PP\u2019 are the required tangents.<\/p>\n<p><br \/>(v) On measuring PM and PP\u2019, we find that PM = PP\u2019 = 4 cm.<br \/>Actual calculation:<br \/>In right angle \u0394OMP, \u2220PMO = 90\u00b0<br \/>\u2234 PM<sup>2<\/sup>\u00a0= OP<sup>2<\/sup>\u00a0\u2013 OM<sup>2<br \/><\/sup>[by Pythagoras theorem i.e. (hypotenuse)<sup>2<\/sup>\u00a0= (base)<sup>2<\/sup>\u00a0+ (perpendicular)<sup>2<\/sup>]<br \/>\u21d2 PM<sup>2<\/sup>\u00a0= (5)<sup>2<\/sup>\u00a0\u2013 (3)<sup>2<\/sup>\u00a0= 25 \u2013 9 = 16<br \/>\u21d2 PM = 4 cm<br \/>Hence, the length of both tangents is 4 cm.<\/p>\n<p>We have provided complete details of RD Sharma Class 10 Solutions Chapter 11 Exercise 11.3. If you have any queries related to <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\"><strong>CBSE<\/strong><\/a>\u00a0Class 10, feel free to ask us in the comment section below.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-rd-sharma-class-10-solutions-chapter-11-exercise-113\"><\/span>FAQs on RD Sharma Class 10 Solutions Chapter 11 Exercise 11.3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1631701002034\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"is-the-rd-sharma-class-10-maths-solutions-chapter-11-exercise-113-available-on-the-kopykitab-website\"><\/span>Is the RD Sharma Class 10 Maths Solutions Chapter 11 Exercise 11.3 available on the Kopykitab website?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, the PDFs of RD Sharma Class 10 Solutions Chapter 11 Exercise 11.3 are available. These solutions are created in a unique method by Kopykitab\u2019s expert faculty.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1631701044790\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"does-rd-sharma-solutions-for-class-10-maths-chapter-11-exercise-113-help-you-to-clear-board-exams\"><\/span>Does RD Sharma Solutions for Class 10 Maths Chapter 11 Exercise 11.3 help you to clear board exams?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, RD Sharma Class 10 Maths Solutions Chapter 11 Exercise 11.3 of Class 10 Maths is an essential chapter. These answers are centered on understanding several Math shortcuts and strategies for quick and easy calculations.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1631701088686\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"where-can-i-get-rd-sharma-class-10-solutions-chapter-11-exercise-113-free-pdf\"><\/span>Where can I get RD Sharma Class 10 Solutions Chapter 11 Exercise 11.3 Free PDF?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can get RD Sharma Class 10 Solutions Chapter 11 Exercise 11.3 Free PDF from the above article.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Class 10 Solutions Chapter 11 Exercise 11.3:\u00a0The construction of tangents to a circle is the key topic covered in this exercise. Students can learn the proper procedures for dealing with difficult problems by approaching RD Sharma Class 10 Solutions. The RD Sharma Solutions for Class 10 Maths Chapter 11 Constructions Exercise 11.3 PDF &#8230; <a title=\"RD Sharma Class 10 Solutions Chapter 11 Constructions Exercise 11.3 (Updated for 2021-22)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-11-exercise-11-3\/\" aria-label=\"More on RD Sharma Class 10 Solutions Chapter 11 Constructions Exercise 11.3 (Updated for 2021-22)\">Read more<\/a><\/p>\n","protected":false},"author":238,"featured_media":127995,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73411,2985,73410],"tags":[3243,9206,73520,4388],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/127983"}],"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\/238"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=127983"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/127983\/revisions"}],"predecessor-version":[{"id":128022,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/127983\/revisions\/128022"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/127995"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=127983"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=127983"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=127983"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}