{"id":4519,"date":"2023-02-15T05:08:20","date_gmt":"2023-02-15T05:08:20","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=4519"},"modified":"2023-02-15T05:13:13","modified_gmt":"2023-02-15T05:13:13","slug":"ncert-solutions-class-9-maths-chapter-10-circles-ex-10-3","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-10-circles-ex-10-3\/","title":{"rendered":"NCERT Solutions Class 9 Maths Chapter 10 Circles Ex 10.3"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 9 Maths\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 10 (Circles)\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 9 Mathematics\u00a0<strong>Chapter &#8211; 10 Circles <\/strong>Exercise 10.3 has been provided here to help the students in solving the questions from this exercise.<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>Chapter 10: Circles<\/strong><\/span><\/p>\n<ul>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-10-circles-ex-10-1\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 10.1<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-10-circles-ex-10-2\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 10.2<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-10-circles-ex-10-4\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 10.4<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-10-circles-ex-10-5\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 10.5<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-10-circles-ex-10-6\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 10.6<\/a><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 10.3<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?<br \/>\n<\/strong><strong>Answer &#8211;\u00a0<\/strong>In this, there are no common points.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-4531\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.3-Ans1i.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"341\" height=\"192\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.3-Ans1i.png 441w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.3-Ans1i-300x169.png 300w\" sizes=\"auto, (max-width: 341px) 100vw, 341px\" \/><br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">In this, there is only one common point.<\/span><br \/>\n<span style=\"color: #000000;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-4532\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.3-Ans1ii.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"484\" height=\"186\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.3-Ans1ii.png 1001w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.3-Ans1ii-300x115.png 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.3-Ans1ii-768x295.png 768w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.3-Ans1ii-480x185.png 480w\" sizes=\"auto, (max-width: 484px) 100vw, 484px\" \/><\/span><br \/>\n<span style=\"color: #000000;\">In this, there are two common points.<\/span><br \/>\n<span style=\"color: #000000;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-4533\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.3-Ans1iii.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"335\" height=\"242\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.3-Ans1iii.png 361w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.3-Ans1iii-300x217.png 300w\" sizes=\"auto, (max-width: 335px) 100vw, 335px\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. Suppose you are given a circle. Give a construction to find its centre.<br \/>\n<\/strong><strong>Answer &#8211;\u00a0<\/strong>Construction:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-4534\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.3-Ans2.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"335\" height=\"373\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.3-Ans2.png 392w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.3-Ans2-269x300.png 269w\" sizes=\"auto, (max-width: 335px) 100vw, 335px\" \/><br \/>\n<strong>Step 1 &#8211;\u00a0<\/strong> Draw a circle with a convenient radius.<\/span><br \/>\n<span style=\"color: #000000;\"><strong>Step 2 &#8211; <\/strong>Draw 2 chords AB and PQ of any length.<\/span><br \/>\n<span style=\"color: #000000;\"><strong>Step 3 &#8211; <\/strong>With A as center and radii\u00a0more than half the length of AB, draw two arcs on opposite sides of\u00a0chord\u00a0AB. With the same radius and with B as center, draw two arcs cutting the former arcs. Join the line. Now DE is the perpendicular bisector of AB.\u00a0<\/span><br \/>\n<span style=\"color: #000000;\"><strong>Step 4 &#8211;<\/strong>\u00a0With P as center and radii more than half the length of PQ, draw two arcs on opposite sides of chord PQ. With the same\u00a0radius\u00a0and with Q as the center, draw two arcs cutting the former arcs. Join the line. Now LM is the\u00a0perpendicular bisector\u00a0of PQ.<\/span><br \/>\n<span style=\"color: #000000;\"><strong>Step 5 &#8211; <\/strong>As the center of the circle should lie both on DE and LM, it is obvious that the intersection points of DE and LM is the center of circle. Mark the intersection points as O.<\/span><br \/>\n<span style=\"color: #000000;\"><strong>Step 6 &#8211;<\/strong>\u00a0O is the required center of the circle.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>3. If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.<br \/>\n<\/strong><strong>Answer &#8211; <\/strong>Let the two circles with centre P and Q intersect at points A and B.<\/span><br \/>\n<span style=\"color: #000000;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-4535\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.3-Ans3.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"350\" height=\"217\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.3-Ans3.png 495w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.3-Ans3-300x186.png 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-10.3-Ans3-480x298.png 480w\" sizes=\"auto, (max-width: 350px) 100vw, 350px\" \/><\/span><br \/>\n<span style=\"color: #000000;\">Join AB.\u00a0 (AB is the common chord.)\u00a0<\/span><br \/>\n<span style=\"color: #000000;\">Join PQ.\u00a0 (AB and PQ bisect each other at M.)<\/span><br \/>\n<span style=\"color: #000000;\">Let M be the midpoint of AB.<\/span><br \/>\n<span style=\"color: #000000;\">Hence, PM\u00a0\u22a5 AB [Since, the line drawn through the centre of a circle to bisect a chord is perpendicular to the chord]<\/span><br \/>\n<span style=\"color: #000000;\">\u2220PMA = 90\u00ba<\/span><br \/>\n<span style=\"color: #000000;\">Now, since M is the midpoint of AB\u00a0<\/span><br \/>\n<span style=\"color: #000000;\">Hence, QM\u00a0\u22a5 AB\u00a0<\/span><br \/>\n<span style=\"color: #000000;\">\u2220QMA = 90\u00ba<\/span><br \/>\n<span style=\"color: #000000;\">Thus,\u00a0\u2220PMQ\u00a0= \u2220PMA + \u2220QMA = 90\u00ba +\u00a090\u00ba =\u00a0180\u00ba<\/span><br \/>\n<span style=\"color: #000000;\">Hence PMQ is a straight line and PMQ\u00a0\u22a5 AB<\/span><br \/>\n<span style=\"color: #000000;\">Therefore,\u00a0\u00a0PMQ is the\u00a0perpendicular\u00a0bisector of the common chord AB and passes through the two centers P and Q.<\/span><br \/>\n<span style=\"color: #000000;\">So, the centres lie on the perpendicular bisector of the common chords.<\/span><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 9 Maths\u00a0 Chapter &#8211; 10 (Circles)\u00a0 The NCERT Solutions in English Language for Class 9 Mathematics\u00a0Chapter &#8211; 10 Circles Exercise 10.3 has been provided here to help the students in solving the questions from this exercise. Chapter 10: Circles NCERT Solution Class 9 Maths Ex &#8211; 10.1 NCERT Solution Class 9 Maths [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[698],"tags":[719,702,186,720,701,5],"class_list":["post-4519","post","type-post","status-publish","format-standard","hentry","category-class-9-maths","tag-class-9th-chapter-10-circles-in-english","tag-ncert-solution-class-9","tag-ncert-solutions","tag-ncert-solutions-class-9-maths-chapter-10-in-english","tag-ncert-solutions-class-9-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>NCERT Solutions Class 9 Maths Chapter 10 Circles Ex 10.3 | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"NCERT Solutions Class 9 Maths\u00a0Chapter - 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