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Class 10 NCERT Solutions Maths Chapter 10 - Circles

Maths is a very important subject if you aim to score good marks in CBSE Grade 10. It gives students an opportunity to boost their overall score. Students who want to get good marks in CBSE Class 10 Mathematics are advised to refer to TopperLearning’s Maths NCERT solutionsfor CBSE Class 10 Maths. It is always beneficial to have solutions handy while practicing. NCERT Solutions for CBSE Class 10 Maths are authored by a special team of subject experts. These are extremely helpful for the preparation of board exams. All the solutions are as per CBSE guidelines. TopperLearning's study material infuses deep knowledge of concepts with the topics. CBSE Class 10 Mathsstudy material is a complete package of the following items ensuring wholesome practice and learning: 


NCERT Solutions for Class 10 Maths Chapter 10 - Circles

In earlier grades, students have been introduced to various concepts that are applied in higher grades. One such concept is Circles. Students are expected to be clear about tangent, secant, radius, diameter, circumference, and other important terms related to a circle. Students are also advised to revise all the theorems about the circle studied in Grade 9. Revise all the basics about a circle using CBSE Class 10 Maths Revision Notes. In this chapter, we will examine the different possibilities when a circle and a line are given in a plane.  We will study the existence of tangents to a circle and also study some of their properties. We will also be proving some interesting properties about the tangents and chords in a circle, which can be understood best with TopperLearning’s elaborated study material.

Students need not worry about the proofs and theorems as CBSE Class 10 Maths video lessonsexplain every concept with absolute clarity. Improve your skills and competency about the Maths  chapter Circles and practise all the important questions from the past year papers and sample papers too. Here is the list of key concepts covered in this chapter:

·         The Tangent to a Circle

·         Number of Tangents from a Point on a Circle

·         Length of the Tangents from the Same Circle

·         Application of the Theorems

The CBSE board expects a 10th grader to be acquainted with all the concepts covered in the chapter Circles. Let’s get an idea about the solutions from each exercise from Class 10 Maths Chapter Circles.

Maths Chapter Circles Chapter 10 - Circles Exercise Ex. 10.1

The circle is the basic concept for many other conical figures. Hence, it is necessary for students to understand each terminology of circle. This chapter is continued in the higher grades in more detail. Students with sound basic knowledge of the concept will find studying circles in higher grades very easy. In addition, this will also increase their scores in Grade 10. 

This exercise in Maths chapter Circles is based on concepts taught in previous classes. Questions from this exercise are asked in the multiple choice question category. Know all the necessary points that need to be mentioned in the answers with Circles NCERT Solutions. Attempt extra questions and objectives with TopperLearning’s CBSE Class 10 Maths sample papers, CBSE Class 10 Maths most important questions and CBSE Class 10 Maths Past Year Papers. If you are stuck on any topic, feel free to reach out to our academic experts using Doubt Solver. Students are also advised to refer to the CBSE Class 10 Maths study material to complete their preparation. 

Maths Chapter Circles Chapter 10 - Circles Exercise Ex. 10.2

Before attempting this exercise, students are also advised to go through the theorems in Mathematics Chapter Circles. TopperLearning’s CBSE Class 10 Maths video lessons are the best resource for learning the theorems. This exercise in Class 10 Maths Chapter Circles is all about the application of the knowledge of tangents in a circle. There are lots of subjective questions asked from Class 10 Maths Chapter Circles. Try solving the questions and refer to the Circles NCERT Solutions for checking your solutions. Every solution is supported with logical, stepwise conceptual insight. The diagrams provide better clarity of the topic in Circles NCERT Solutions.

Enhance your practice by picking up questions from TopperLearning’s CBSE Class 10 Maths sample papers, CBSE Class 10 Maths most important questions and  CBSE Class 10 Maths Past Year Papers.

Circles Exercise Ex. 10.1

Solution 1

Solution 2

Solution 3

Solution 4

Circles Exercise Ex. 10.2

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Since, ABCD is a parallelogram,

AB = CD                                                                (i)

BC = AD                                                                (ii)

Now, it can be observed that:

DR = DS                 (tangents on circle from point D)

CR = CQ                 (tangents on circle from point C)

BP = BQ                 (tangents on circle from point B)

AP = AS                 (tangents on circle from point A)

Adding all the above four equations,

DR + CR + BP + AP = DS + CQ + BQ + AS

(DR + CR) + (BP + AP) = (DS + AS) + (CQ + BQ)                 

CD + AB = AD + BC                                            (iii)


From equation (i) (ii)  and (ii):

         2AB = 2BC

         AB = BC

         AB = BC = CD = DA

         Hence, ABCD is a rhombus.

Solution 12

Solution 13