{"id":122727,"date":"2022-02-20T11:44:13","date_gmt":"2022-02-20T06:14:13","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=122727"},"modified":"2024-02-21T15:19:55","modified_gmt":"2024-02-21T09:49:55","slug":"ncert-exemplar-solutions-for-class-9-maths-chapter-10-circles-infinity-learn","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-10-circles\/","title":{"rendered":"NCERT Exemplar Solutions for Class 9 Maths Chapter 10 Circles &#8211; Infinity Learn"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 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\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" 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: #999;color:#999\" 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\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-10-circles\/#NCERT_Exemplar_Solutions_for_Class_9_Maths_Chapter_10_Circles_-_Infinity_Learn\" title=\"NCERT Exemplar Solutions for Class 9 Maths Chapter 10 Circles &#8211; Infinity Learn\">NCERT Exemplar Solutions for Class 9 Maths Chapter 10 Circles &#8211; Infinity Learn<\/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:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-10-circles\/#Key_Features_of_NCERT_Exemplar_Solutions_for_Class_9_Maths_Chapter_10-_Circles\" title=\"Key Features of NCERT Exemplar Solutions for Class 9 Maths Chapter 10- Circles\">Key Features of NCERT Exemplar Solutions for Class 9 Maths Chapter 10- Circles<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-10-circles\/#NCERT_Exemplar_Class_9_Maths_Chapter_5_Exercise_51\" title=\"NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.1\">NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-10-circles\/#NCERT_Exemplar_Class_9_Maths_Chapter_5_Exercise_52\" title=\"NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.2\">NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-10-circles\/#NCERT_Exemplar_Class_9_Maths_Chapter_5_Exercise_53\" title=\"NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.3\">NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-10-circles\/#NCERT_Exemplar_Class_9_Maths_Chapter_5_Exercise_54\" title=\"NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.4\">NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.4<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-10-circles\/#FAQs\" title=\"FAQ&#8217;s\">FAQ&#8217;s<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-10-circles\/#Q_How_are_NCERT_Exemplar_Solutions_for_Class_9_Maths_Chapter_10_helpful_for_Class_9_students\" title=\"Q. How are NCERT Exemplar Solutions for Class 9 Maths Chapter 10 helpful for Class 9 students?\">Q. How are NCERT Exemplar Solutions for Class 9 Maths Chapter 10 helpful for Class 9 students?<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-10-circles\/#Q_Why_should_we_follow_NCERT_Exemplar_Solutions_for_Class_9_Maths_Chapter_10\" title=\"Q. Why should we follow NCERT Exemplar Solutions for Class 9 Maths Chapter 10?\">Q. Why should we follow NCERT Exemplar Solutions for Class 9 Maths Chapter 10?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-10-circles\/#Q_Where_to_download_NCERT_Exemplar_Solutions_for_Class_9_Maths_Chapter_10\" title=\"Q. Where to download NCERT Exemplar Solutions for Class 9 Maths Chapter 10?\">Q. Where to download NCERT Exemplar Solutions for Class 9 Maths Chapter 10?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>Circles are provided here in PDF format, which can be downloaded for free. The <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/\"><strong>NCERT Exemplar Solutions<\/strong><\/a> for this chapter Circles is included for the second term as per the latest update of the term-wise CBSE curriculum (2021-22) and has been designed by our expert teachers with 100 percent accuracy.<\/p>\n<p>All the solved questions of Chapter 10 Circles, are with respect to the second term <a href=\"https:\/\/infinitylearn.com\/surge\/cbse\/cbse-syllabus\/\"><strong>CBSE syllabus<\/strong><\/a> and guidelines, to help students solve each exercise question present in the book and prepare for the exam. These serve as reference tools for the students to do homework and also support them to score good marks. Students can also get the solutions for Class 9th Maths all chapters exercise-wise and practice well for the second term exams.<\/p>\n<p>Chapter 10, Circles, of Grade 9, is one of the most important chapters, whose concepts will also be used in Class 10. The weightage of this chapter in the final exam is around 15 marks. Therefore, students are advised to read the chapter carefully and practice each and every question included in the textbook with the help of NCERT Exemplar Solutions along with examples, to have good practice.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Exemplar_Solutions_for_Class_9_Maths_Chapter_10_Circles_-_Infinity_Learn\"><\/span>NCERT Exemplar Solutions for Class 9 Maths Chapter 10 Circles &#8211; Infinity Learn<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"Key_Features_of_NCERT_Exemplar_Solutions_for_Class_9_Maths_Chapter_10-_Circles\"><\/span>Key Features of NCERT Exemplar Solutions for Class 9 Maths Chapter 10- Circles<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>The solutions for the chapter-Circles work as a reference for the students.<\/li>\n<li>Students will be able to resolve all the problems of this chapter in a faster way.<\/li>\n<li>It is good learning material for exam preparation and to do the revision for Class 9 Maths Chapter 10.<\/li>\n<li>The questions of Circles are solved by our subject experts.<\/li>\n<li>The NCERT Exemplar Solutions are given as per the latest update on the CBSE syllabus and guidelines.<\/li>\n<\/ul>\n<p><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-9\/\" target=\"_blank\" rel=\"noopener\"><button class=\"favorite styled\" style=\"width: 100%;\" type=\"button\"> <input class=\"more\" type=\"button\" value=\"Also Read!\" \/> <strong>NCERT Solutions for Class 9<\/strong><\/button><\/a><\/p>\n<article class=\"post-79029 post type-post status-publish format-standard category-cbse entry\" aria-label=\"NCERT Exemplar Class 9 Maths Chapter 5 Introduction to Euclid\u2019s Geometry\">\n<div class=\"entry-content\">\n<h3><span class=\"ez-toc-section\" id=\"NCERT_Exemplar_Class_9_Maths_Chapter_5_Exercise_51\"><\/span>NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Question 1.<br \/>\nThe three steps from solids to points are:<br \/>\n(A) Solids-surfaces-lines-points<br \/>\n(B) Solids-lines-surfaces-points<br \/>\n(C) Lines-points-sucfaces-solids<br \/>\n(D) Lines-surfaces-points-solids<br \/>\nSolution:<br \/>\n(A): The three steps from solids to points are solids-surfaces-lines-points.<\/p>\n<p>Question 2.<br \/>\nThe number of dimensions, a solid has:<br \/>\n(A) 1<br \/>\n(B) 2<br \/>\n(C) 3<br \/>\n(D) 0<br \/>\nSolution:<br \/>\n(C): A solid e.g., Cuboid has shape, size, and position. So, solid has three dimensions.<\/p>\n<p>Question 3.<br \/>\nThe number of dimensions, a surface has:<br \/>\n(A) 1<br \/>\n(B) 2<br \/>\n(C) 3<br \/>\n(D) 0<br \/>\nSolution:<br \/>\n(B): Boundaries of a solid are called surfaces. A surface (plane) has only length and breadth. So, it has two dimensions.<\/p>\n<p>Question 4.<br \/>\nThe number of dimension, a point has<br \/>\n(A) 0<br \/>\n(B) 1<br \/>\n(C) 2<br \/>\n(D) 3<br \/>\nSolution:<br \/>\n(A): A point is that which has no part<br \/>\ni. e., no length, no breadth and no height. So, it has no dimension.<\/p>\n<p>Question 5.<br \/>\nEuclid divided his famous treatise \u201cThe Elements\u201d into<br \/>\n(A) 13 chapters<br \/>\n(B) 12 chapters<br \/>\n(C) 11 chapters<br \/>\n(D) 9 chapters<br \/>\nSolution:<br \/>\n(A): Euclid divided his famous treatise \u2018The Elements\u201d into 13 chapters.<\/p>\n<p>Question 6.<br \/>\nThe total number of propositions in the Elements are<br \/>\n(A) 465<br \/>\n(B) 460<br \/>\n(C) 13<br \/>\n(D) 55<br \/>\nSolution:<br \/>\n(A): The statements that can be proved are called propositions or theorems. Euclid deduced 465 propositions in a logical chain using his axioms, postulates, definitions and theorems.<\/p>\n<p>Question 7.<br \/>\nBoundaries of solids are:<br \/>\n(A) surfaces<br \/>\n(B) curves<br \/>\n(C) lines<br \/>\n(D) points<br \/>\nSolution:<br \/>\n(A): Boundaries of solids are surfaces.<\/p>\n<p>Question 8.<br \/>\nBoundaries of surfaces are:<br \/>\n(A) surfaces<br \/>\n(B) curves<br \/>\n(C) lines<br \/>\n(D) points<br \/>\nSolution:<br \/>\n(B) : The boundaries of surfaces are curves.<\/p>\n<p>Question 9.<br \/>\nIn Indus Valley Civilisation (about 3000 B.C.), the bricks used for construction work were having dimensions in the ratio<br \/>\n(A) 1 : 3 : 4<br \/>\n(B) 4 : 2 : 1<br \/>\n(C) 4 : 4 : 1<br \/>\n(D) 4 : 3 : 2<br \/>\nSolution:<br \/>\n(B) : In Indus Valley Civilisation, the bricks used for construction work were having dimensions in the ratio length : breadth : thickness = 4 : 2 : 1.<\/p>\n<p>Question 10.<br \/>\nA pyramid is a solid figure, the base of which is<br \/>\n(A) only a triangle<br \/>\n(B) only a square<br \/>\n(C) only a rectangle<br \/>\n(D) any polygon<br \/>\nSolution:<br \/>\n(D) : A pyramid is a solid figure, the base of which is a triangle or square or some other polygon.<\/p>\n<p>Question 11.<br \/>\nThe side faces of a pyramid are<br \/>\n(A) Triangles<br \/>\n(B) Squares<br \/>\n(C) Polygons<br \/>\n(D) Trapeziums<br \/>\nSolution:<br \/>\n(A) : The side faces of a pyramid are always triangles.<\/p>\n<p>Question 12.<br \/>\nIt is known that, if x + y = 10, then x + y + z = 10 + z. The Euclid\u2019s axiom that illustrates this statement is:<br \/>\n(A) First Axiom<br \/>\n(B) Second Axiom<br \/>\n(C) Third Axiom<br \/>\n(D) Fourth Axiom<br \/>\nSolution:<br \/>\nThe Euclid\u2019s axiom that illustrates the given statement is second axiom. According to this, if equals are added to equals, the wholes are equal.<\/p>\n<div class=\"google-auto-placed ap_container\"><\/div>\n<p>Question 13.<br \/>\nIn ancient India, the shapes of altars used for household rituals were:<br \/>\n(A) Squares and circles<br \/>\n(B) Triangles and rectangles<br \/>\n(C) Trapeziums and pyramids<br \/>\n(D) Rectangles and squares<br \/>\nSolution:<br \/>\n(A) : In ancient India, squares and circular altars were used for household rituals.<\/p>\n<p>Question 14.<br \/>\nThe number of interwoven isosceles triangles in Sriyantra (in the Atharvaveda) is:<br \/>\n(A) Seven<br \/>\n(B) Eight<br \/>\n(C) Nine<br \/>\n(D) Eleven<br \/>\nSolution:<br \/>\n(C): The Sriyantra (in the Atharvaveda) consists of nine interwoven isosceles triangles.<\/p>\n<p>Question 15.<br \/>\nGreek\u2019s emphasised on:<br \/>\n(A) Inductive reasoning<br \/>\n(B) Deductive reasoning<br \/>\n(C) Both (A) and (B)<br \/>\n(D) Practical use of geometry<br \/>\nSolution:<br \/>\n(B) : Greek\u2019s emphasised on deductive reasoning.<\/p>\n<p>Question 16.<br \/>\nIn ancient India, altars with combination of shapes like rectangles, triangles and trapeziums were used for<br \/>\n(A) Public worship<br \/>\n(B) Household rituals<br \/>\n(C) Both (A) and (B)<br \/>\n(D) None of A, B, C<br \/>\nSolution:<br \/>\n(A): In ancient India altars whose shapes were combinations of rectangles, triangles and trapeziums were used for public worship.<\/p>\n<p>Question 17.<br \/>\nEuclid belongs to the country:<br \/>\n(A) Babylonia<br \/>\n(B) Egypt<br \/>\n(C) Greece<br \/>\n(D) India<br \/>\nSolution:<br \/>\n(C) : Euclid belongs to the country Greece.<\/p>\n<p>Question 18.<br \/>\nThales belongs to the country:<br \/>\n(A) Babylonia<br \/>\n(B) Egypt<br \/>\n(C) Greece<br \/>\n(D) Rome<br \/>\nSolution:<br \/>\n(C) : Thales belongs to the country Greece.<\/p>\n<p>Question 19.<br \/>\nPythagoras was a student of:<br \/>\n(A) Thales<br \/>\n(B) Euclid<br \/>\n(C) Both (A) and (B)<br \/>\n(D) Archimedes<br \/>\nSolution:<br \/>\n(A) : Pythagoras was a student of Thales.<\/p>\n<p>Question 20.<br \/>\nWhich of the following needs a proof ?<br \/>\n(A) Theorem<br \/>\n(B) Axiom<br \/>\n(C) Definition<br \/>\n(D) Postulate<br \/>\nSolution:<br \/>\n(A): The statements that needs a proof are called propositions or theorems.<\/p>\n<p>Question 21.<br \/>\nEuclid stated that all right angles are equal to each other in the form of<br \/>\n(A) an axiom<br \/>\n(B) a definition<br \/>\n(C) a postulate<br \/>\n(D) a proof<br \/>\nSolution:<br \/>\n(C) : Euclid stated that all right angles are equal to each other in the form of a postulate.<\/p>\n<p>Question 22.<br \/>\n\u2018Lines are parallel, if they do not intersect\u2019 is stated in the form of<br \/>\n(A) an axiom<br \/>\n(B) a definition<br \/>\n(C) a postulate<br \/>\n(D) a proof<br \/>\nSolution:<br \/>\n(B) : \u2018Lines are parallel, if they do not intersect\u2019 is the definition of parallel lines.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"NCERT_Exemplar_Class_9_Maths_Chapter_5_Exercise_52\"><\/span>NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Question 1.<br \/>\nEuclidean geometry is valid only for curved surfaces<br \/>\nSolution:<br \/>\nFalse<br \/>\nBecause Euclidean geometry is valid only for the figures in the plane but on the curved surfaces, it fails.<\/p>\n<p>Question 2.<br \/>\nThe boundaries of the solids are curves.<br \/>\nSolution:<br \/>\nBecause the boundaries of the solids are surfaces.<\/p>\n<p>Question 3.<br \/>\nThe edges of a surface are curves.<br \/>\nSolution:<br \/>\nFalse<br \/>\nBecause the edges of surfaces are lines.<\/p>\n<p>Question 4.<br \/>\nThe things which are double of the same thing are equal to one another<br \/>\nSolution:<br \/>\nTrue<br \/>\nSince, it is one of the Euclid\u2019s axiom.<\/p>\n<p>Question 5.<br \/>\nIf a quantity B is a part of another quantity A, then A can be written as the sum of B and some third quantity C.<br \/>\nSolution:<br \/>\nTrue<br \/>\nSince, it is one of the Euclid\u2019s axiom.<\/p>\n<p>Question 6.<br \/>\nThe statements that are proved are called axioms.<br \/>\nSolution:<br \/>\nFalse<br \/>\nBecause the statements that are proved are called theorems.<\/p>\n<p>Question 7.<br \/>\n\u201cFor every line l and for every point P not lying on a given line l, there exits a unique line m passing though P and parallel to l is known as Playfair\u2019s axiom.<br \/>\nSolution:<br \/>\nTrue<br \/>\nSince, it is an equivalent version of Euclid\u2019s fifth postulate and it is known as Playfair\u2019s axiom.<\/p>\n<p>Question 8.<br \/>\nTwo distinct intersecting lines cannot be parallel to the same line.<br \/>\nSolution:<br \/>\nTrue<br \/>\nSince, it is an equivalent version of Euclid\u2019s fifth postulate.<\/p>\n<p>Question 9.<br \/>\nAttempt to prove Euclid\u2019s fifth postulate using the other postulates and axioms led to the discovery of several other geometries.<br \/>\nSolution:<br \/>\nTrue<br \/>\nAll attempts to prove the fifth postulate as a theorem led to a great achievement in the creation of several other geometries. These geometries are quite different from Euclidean geometry and are called non-Euclidean geometry.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"NCERT_Exemplar_Class_9_Maths_Chapter_5_Exercise_53\"><\/span>NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.3<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Question 1.<\/strong><br \/>\nTwo salesmen make equal sales during the month of August. In September, each salesmen doubles his sale of the month of August. Compare their sales in September.<br \/>\n<strong>Solution:<\/strong><br \/>\nLet the equal sales of two salesmen in August be y. In September, each salesman doubles his sale of August.<\/p>\n<p>Thus, sale of first salesman is 2y and sale of second salesman is 2y.<\/p>\n<p>According to Euclid\u2019s axioms, things which are double of the same things are equal to one another.<\/p>\n<p>So, in September their sales are again equal.<\/p>\n<p><strong>Question 2.<\/strong><br \/>\nIt is known that x + y = 10 and that x = z. Show that z + y = 10.<br \/>\n<strong>Solution:<\/strong><br \/>\nWe have, x + y = 10 \u2026(i)<br \/>\nand x = z \u2026(ii)<br \/>\nOn adding y to both sides, we have x + y = z + y \u2026. (iii)<br \/>\n[ \u2235 If equals are added to equals, the wholes are equal] From (i) and (iii), we get z + y = 10<\/p>\n<p><strong>Question 3.<\/strong><br \/>\nLook at the given figure. Show that length AH &gt; sum of lengths of AB + BC + CD.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708284\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-1.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-1\" width=\"234\" height=\"37\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\nFrom the given figure, we have<br \/>\nAB + BC + CD = AD<br \/>\n[AB, BC and CD are the parts of AD]\nSince, AD is also the part of AH.<br \/>\nAH &gt; AD [ \u2235 The whole is greater than the part]\nSo, length AH &gt; sum of lengths of AB + BC + CD.<\/p>\n<p><strong>Question 4.<\/strong><br \/>\nIn the given figure, we have AB = BC, BX = BY. Show that AX = CY.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708285\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-2.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-2\" width=\"116\" height=\"111\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\nGiven, AB = BC \u2026(i)<br \/>\nand BX = BY \u2026(ii)<br \/>\nOn subtracting (ii) from (i), we get AB \u2013 BX = BC \u2013 BY<br \/>\n[\u2235 If equals are subtracted from equals, the remainders are equal]\n\u2234 AX = CY<\/p>\n<p><strong>Question 5.<\/strong><br \/>\nIn the given figure, we have X and Y are the mid-points of AC and BC and AX = CY. Show that AC = BC.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708286\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-3.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-3\" width=\"108\" height=\"113\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\nWe have, X is the mid-point of AC.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708287\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-4.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-4\" width=\"337\" height=\"249\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-4.png 337w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-4-300x222.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><\/p>\n<p><strong>Question 6.<\/strong><br \/>\nIn the given figure, we have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708288\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-5-300x152-1.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-5\" width=\"300\" height=\"152\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708289\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-6.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-6\" width=\"336\" height=\"166\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-6.png 336w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-6-300x148.png 300w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><\/p>\n<p><strong>Question 7.<\/strong><br \/>\nIn the given figure, we have \u22201 = \u22202 and \u22202 = \u22203. Show that \u22201 = \u22203.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708290\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-7.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-7\" width=\"184\" height=\"184\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-7.png 184w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-7-150x150.png 150w\" sizes=\"(max-width: 184px) 100vw, 184px\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\nWe have, \u22201 = \u22202 and \u22202 = \u22203 \u21d2 \u22201 = \u22203 [ \u2235 Things which are equal to the same thing are equal to one another]\n<p><strong>Question 8.<\/strong><br \/>\nIn the given figure, we have \u22201 = \u22203 and \u22202 = \u22204. Show that \u2220A = \u2220C.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708291\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-8.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-8\" width=\"180\" height=\"179\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-8.png 180w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-8-150x150.png 150w\" sizes=\"(max-width: 180px) 100vw, 180px\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\nGiven \u22201 = \u22203 \u2026(i)<br \/>\n\u22202 = \u22204 \u2026(ii)<br \/>\nAdding (i) and (ii), we get \u22201 + \u22202 = \u22203 + \u22204<br \/>\n[\u2235 If equals are added to equals, then wholes are also equal]\n\u21d2 \u2220A = \u2220C<\/p>\n<p><strong>Question 9.<\/strong><br \/>\nIn the given figure, we have \u2220ABC = \u2220ACB, \u22203 = \u22204. Show that \u22201 = \u22202.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708292\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-9.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-9\" width=\"102\" height=\"110\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\nGiven \u2220ABC = \u2220ACB \u2026(i)<br \/>\nand \u2220A = \u22203 \u2026(ii)<br \/>\nSubtracting (ii) from (i), we get \u2220ABC \u2013 \u22204 = \u2220ACB \u2013 \u22203<br \/>\n[ \u2235 If equals are subtracted from equals, then remainders are also equal]\n\u21d2 \u22201 = \u22202<\/p>\n<p><strong>Question 10.<\/strong><br \/>\nIn the given figure, we have AC = DC, CB = CE. Show that AB = DE.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708293\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-10.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-10\" width=\"232\" height=\"163\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\nWe have, AC = DC \u2026(i)<br \/>\nand CB = CE \u2026(ii)<br \/>\nAdding (i) and (ii), we get<br \/>\nAC + CB = DC + CE<br \/>\n[ \u2235 If equals are added to equals, then wholes are also equal]\n\u21d2 AB = DE<\/p>\n<p><strong>Question 11.<\/strong><br \/>\nIn the given figure, if OX = <span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mn\">1<span id=\"MathJax-Span-5\" class=\"mn\">2XY, PX = <span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mfrac\"><span id=\"MathJax-Span-9\" class=\"mn\">1<span id=\"MathJax-Span-10\" class=\"mn\">2XZ and OX= PX, show that XY= XZ<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708294\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-11.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-11\" width=\"102\" height=\"116\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\nGiven OX = <span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mfrac\"><span id=\"MathJax-Span-14\" class=\"mn\">1<span id=\"MathJax-Span-15\" class=\"mn\">2XY \u21d2 20X = XY \u2026(i)<br \/>\nPX = <span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-16\" class=\"math\"><span id=\"MathJax-Span-17\" class=\"mrow\"><span id=\"MathJax-Span-18\" class=\"mfrac\"><span id=\"MathJax-Span-19\" class=\"mn\">1<span id=\"MathJax-Span-20\" class=\"mn\">2XZ \u21d2 2PX = XZ \u2026(ii)<br \/>\nand OX = PX \u2026(iii)<br \/>\nmultiplying (iii) by 2, we get<br \/>\n2OX = 2PX<br \/>\n[\u2235 Things which are double of the same things are equal to one another]\n\u21d2 XY = XZ [From (i) and (ii)]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mn\"><span id=\"MathJax-Span-5\" class=\"mn\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mfrac\"><span id=\"MathJax-Span-9\" class=\"mn\"><span id=\"MathJax-Span-10\" class=\"mn\"><span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mfrac\"><span id=\"MathJax-Span-14\" class=\"mn\"><span id=\"MathJax-Span-15\" class=\"mn\"><span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-16\" class=\"math\"><span id=\"MathJax-Span-17\" class=\"mrow\"><span id=\"MathJax-Span-18\" class=\"mfrac\"><span id=\"MathJax-Span-19\" class=\"mn\"><span id=\"MathJax-Span-20\" class=\"mn\"><strong>Question 12.<\/strong><br \/>\nIn the given figure<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708295\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-12.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-12\" width=\"172\" height=\"145\" \/><br \/>\n(i) AB = BC, M is the mid-point of AB and N is the mid-point of BC. Show that AM = NC.<br \/>\n(ii) BM = BN, M is the mid-point of AB and N is the mid-point of BC. Show that AB = BC.<br \/>\n<strong>Solution:<\/strong><br \/>\n(i): Given, AB = BC \u2026(1)<br \/>\nM is the mid-point of AB.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708296\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-13-300x41-1.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-13\" width=\"300\" height=\"41\" \/><br \/>\nand N is the mid-point of BC.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708297\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-14-300x42-1.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-14\" width=\"300\" height=\"42\" \/><br \/>\nMultiplying both sides of (1) by <span id=\"MathJax-Element-5-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-21\" class=\"math\"><span id=\"MathJax-Span-22\" class=\"mrow\"><span id=\"MathJax-Span-23\" class=\"mfrac\"><span id=\"MathJax-Span-24\" class=\"mn\">1<span id=\"MathJax-Span-25\" class=\"mn\">2, we get<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708298\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-15.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-15\" width=\"90\" height=\"41\" \/><br \/>\n[ \u2235 Things which are halves of the same things are equal to one another]\n\u21d2 AM = NC [Using (2) and (3)]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>(ii) Given, BM = BN \u2026(1)<br \/>\nM is the mid-point of AB.<br \/>\n\u2234 AM = BM = <span id=\"MathJax-Element-6-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-26\" class=\"math\"><span id=\"MathJax-Span-27\" class=\"mrow\"><span id=\"MathJax-Span-28\" class=\"mfrac\"><span id=\"MathJax-Span-29\" class=\"mn\">1<span id=\"MathJax-Span-30\" class=\"mn\">2AB<br \/>\n\u21d2 2AM = 2BM = AB \u2026(2)<br \/>\nand N is the mid-point of BC.<br \/>\n\u2234 BN = NC = <span id=\"MathJax-Element-7-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-31\" class=\"math\"><span id=\"MathJax-Span-32\" class=\"mrow\"><span id=\"MathJax-Span-33\" class=\"mfrac\"><span id=\"MathJax-Span-34\" class=\"mn\">1<span id=\"MathJax-Span-35\" class=\"mn\">2BC<br \/>\n\u21d2 2BN = 2NC = BC \u2026(3)<br \/>\nmultiplying both sides of (1) by 2, we get<br \/>\n2 BM = 2 BN<br \/>\n[ \u2235 Things which are double of the same thing are equal to one another]\n\u21d2 AB = BC [Using (2) and (3)]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"NCERT_Exemplar_Class_9_Maths_Chapter_5_Exercise_54\"><\/span>NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.4<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Question 1.<br \/>\nRead the following statement:<br \/>\nAn equilateral triangle is a polygon made up of three line segments out of which two line segments are equal to the third one and all its angles are 60\u00b0 each.<br \/>\nDefine the terms used in this definition which you feel necessary. Are there any undefined terms in this? Can you justify that all sides and all angles are equal in a equilateral triangle.<br \/>\nSolution:<br \/>\nThe terms need to be defined are<\/p>\n<ul>\n<li>Polygon : A closed figure bounded by three or more line Segments.<\/li>\n<li>Line segment : Part of a line with two end points.<\/li>\n<li>Line: Undefined term.<\/li>\n<li>Point: Undefined term.<\/li>\n<li>Angle: A figure formed by two rays with one common initial point.<\/li>\n<li>Acute angle : Angle whose measure is between 0\u00b0 to 90\u00b0.<\/li>\n<\/ul>\n<p>Here undefined terms are line and point.<br \/>\nAll the angles of equilateral triangle are 60\u00b0 each (given).<\/p>\n<p>Two line segments are equal to the third one (given).<\/p>\n<p>\u201cAccording to Euclid\u2019s axiom, \u201cthings which are equal to the same things are equal to one another\u201d, we conclude that all three sides of an equilateral triangle are equal.<\/p>\n<p>Question 2.<br \/>\nStudy the following statements:<br \/>\n\u201cTwo intersecting lines cannot be perpendicular to the same line.\u201d Check whether it is an equivalent version to the Euclid\u2019s fifth postulate.<br \/>\n[Hint: Identify the two intersecting lines \/ and m and the line n in the above statement.]\nSolution:<br \/>\nTwo equivalent versions of Euclid\u2019s fifth postulate are as follows:<br \/>\n(i) For every line l and for every point P not lying on l, there exists a unique line m passing through P and parallel to l.<br \/>\n(ii) Two distinct intersecting lines cannot be parallel to the same line.<\/p>\n<p>From above two statements it is clear that given statement is not an equivalent version to the Euclid\u2019s fifth postulate.<\/p>\n<p>Question 3.<br \/>\nRead the following statements which are taken as axioms:<br \/>\n(i) If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal.<br \/>\n(ii) If a transversal intersect two parallel lines, then alternate interior angles are equal.<br \/>\nIs this system of axioms consistent ? Justify your answer.<br \/>\nSolution:<br \/>\nAs we know that, if a transversal intersects two parallel lines, then each pair of corresponding angles are equal, then first is false, so, not an axiom.<\/p>\n<p>Also, if a transversal intersects two parallel lines, then each pair of alternate interior angles are equal, then second is true so, it is an axiom.<\/p>\n<p>So, in given statements, first is false and second is an axiom.<\/p>\n<p>Thus, given system of axioms is not consistent.<\/p>\n<p>Question 4.<br \/>\nRead the following two statements which are taken as axioms:<br \/>\n(i) If two lines intersect each other, then the vertically opposite angles are not equal.<br \/>\n(ii) If a ray stands on a line, then the sum of two adjacent angles, so formed is equal to 180\u00b0.<br \/>\nIs this system of axioms consistent ? Justify your answer.<br \/>\nSolution:<br \/>\nAs we know that, if two lines intersect each other, then the vertically opposite angles are equal, then first is false, so, not an axiom. Also, if a ray stands on a line, then the sum of two adjacent angles so formed is equal to 180\u00b0, then second is true so, it is an axiom.<\/p>\n<p>So, in given statements, first is false and second is an axiom. Thus, given system of axioms is not consistent.<\/p>\n<p>Question 5.<br \/>\nRead the following axioms:<br \/>\n(i) Things which are equal to the same thing are equal to one another.<br \/>\n(ii) If equals are added to equals, the wholes are equal.<br \/>\n(iii) Things which are double of the same thing are equal to one another.<br \/>\nCheck whether the given system of axioms is consistent or inconsistent.<br \/>\nSolution:<br \/>\nSince, the given three axioms are Euclid\u2019s axioms.<\/p>\n<\/div>\n<\/article>\n<p>&nbsp;<\/p>\n<h2><span class=\"ez-toc-section\" id=\"FAQs\"><\/span>FAQ&#8217;s<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h2><span class=\"ez-toc-section\" id=\"Q_How_are_NCERT_Exemplar_Solutions_for_Class_9_Maths_Chapter_10_helpful_for_Class_9_students\"><\/span><span style=\"font-size: 12pt; color: #0000ff;\">Q. How are NCERT Exemplar Solutions for Class 9 Maths Chapter 10 helpful for Class 9 students?<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"color: #ff0000;\"><strong>Ans:<\/strong> NCERT Exemplar Solutions for Class 9 Maths Chapter 10 are used by students to get a proper grasp of all the concepts of the subjects and also to lay the foundation for their career or further higher studies. Infinity Learn&#8217;s experts formulate these questions in an easy and understandable manner that helps students solve problems in the most efficient possible ways. We hope these solutions will help CBSE Class 9 students to build a strong foundation of the basics and secure excellent marks in their final exam.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Q_Why_should_we_follow_NCERT_Exemplar_Solutions_for_Class_9_Maths_Chapter_10\"><\/span><span style=\"font-size: 12pt; color: #0000ff;\">Q. Why should we follow NCERT Exemplar Solutions for Class 9 Maths Chapter 10?<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #ff0000;\"><strong>Ans:<\/strong> NCERT Exemplar Solutions for Class 9 Maths Chapter 10 is the correct learning strategy that is devised to help them master the concepts. Revising from the solutions, along with the textbooks, will help students crack any problems asked in the second term exams. These solutions help to boost the problem-solving skills of the students, along with their logical reasoning. These are the most popular study materials used by the students to refer for the CBSE term-wise exams. Practicing these solutions help the students to top the final term exams and ace the subject.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Q_Where_to_download_NCERT_Exemplar_Solutions_for_Class_9_Maths_Chapter_10\"><\/span><span style=\"font-size: 12pt; color: #0000ff;\">Q. Where to download NCERT Exemplar Solutions for Class 9 Maths Chapter 10?<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #ff0000;\"><strong>Ans:<\/strong> NCERT Exemplar Solutions for Class 9 Maths Chapter 10 can be downloaded by the students in offline mode or can be referred to online from the Infinity Learn website. These solutions are formulated by Infinity Learn expert faculty, which are present in the NCERT textbook of Class 9 Maths. These are according to the latest term-wise CBSE syllabus.<\/span><\/p>\n<p>For more visit <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/physics\/chapter-9-mechanical-properties-of-solids\/\">NCERT Exemplar Solutions for Class 11 Physics Chapter 9 &amp;#8211; Mechanical Properties of Solids<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Circles are provided here in PDF format, which can be downloaded for free. The NCERT Exemplar Solutions for this chapter [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Free PDF download of NCERT Exemplar Solutions for Class 9 Maths Chapter 10 Circles solved by expert Maths teachers on Infinitylearn.com as per NCERT (CBSE) Book guidelines. All Chapter 10 Circles exercise questions with solutions to help you to revise complete syllabus and score more marks in your examinations.","custom_permalink":"study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-10-circles\/"},"categories":[152,159,105,21],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Exemplar Solutions for Class 9 Maths Chapter 10 Circles - Infinity Learn - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Free PDF download of NCERT Exemplar Solutions for Class 9 Maths Chapter 10 Circles solved by expert Maths teachers on Infinitylearn.com as per NCERT (CBSE) Book guidelines. All Chapter 10 Circles exercise questions with solutions to help you to revise complete syllabus and score more marks in your examinations.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-10-circles\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Exemplar Solutions for Class 9 Maths Chapter 10 Circles - Infinity Learn - Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"og:description\" content=\"Free PDF download of NCERT Exemplar Solutions for Class 9 Maths Chapter 10 Circles solved by expert Maths teachers on Infinitylearn.com as per NCERT (CBSE) Book guidelines. All Chapter 10 Circles exercise questions with solutions to help you to revise complete syllabus and score more marks in your examinations.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-10-circles\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:published_time\" content=\"2022-02-20T06:14:13+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-02-21T09:49:55+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-1.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Prasad Gupta\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"17 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"NCERT Exemplar Solutions for Class 9 Maths Chapter 10 Circles - Infinity Learn - Infinity Learn by Sri Chaitanya","description":"Free PDF download of NCERT Exemplar Solutions for Class 9 Maths Chapter 10 Circles solved by expert Maths teachers on Infinitylearn.com as per NCERT (CBSE) Book guidelines. 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