NCERT Solutions for Exercise 10.2 Class 9 Maths Chapter 10

NCERT Solutions for Exercise 10.2 Class 9 Maths Chapter 10 - Circles

Edited By Safeer PP | Updated on Jul 29, 2022 06:32 PM IST

NCERT Solutions for Class 9 Maths chapter 10 exercise 10.2 is about angle subtended by a chord at a point. A circle is a two-dimensional geometrical form in which all points on the surface of the circle are equidistant from the radius, which is the centre point. A circle's chord is the line segment that connects two locations on its circumference. You will see that the angles subtended by two or more equal chords of a circle at the centre are equal if you draw two or more equal chords of a circle and determine the angles they occupied in the centre. In the NCERT solutions for Class 9 Maths chapter 10 exercise 10.2, we will cover the theorems pertaining to the angle subtended by a chord at a point in depth. The following exercise are also included in NCERT book Class 9 Mathematics chapter 10 exercise 10.1.

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Circles Class 9 Chapter 10 Circles Exercise: 10.2
More About NCERT Solutions for Class 9 Maths Exercise 10.2
Benefits of NCERT Solutions for Class 9 Maths Exercise 10.2
NCERT Solutions of Class 10 Subject Wise
Subject Wise NCERT Exemplar Solutions

Circles Class 9 Chapter 10 Circles Exercise: 10.2

Q1 Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

Answer:

Given: The two circles are congruent if they have the same radii.

To prove: The equal chords of congruent circles subtend equal angles at their centres i.e. $\angle$ BAC= $\angle$ QPR

Proof :

1640237118228

In $\triangle$ ABC and $\triangle$ PQR,

BC = QR (Given)

AB = PQ (Radii of congruent circle)

AC = PR (Radii of congruent circle)

Thus, $\triangle$ ABC $\cong$ $\triangle$ PQR (By SSS rule)

$\angle$ BAC= $\angle$ QPR (CPCT)

Q2 Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

Answer:

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Given : chords of congruent circles subtend equal angles at their centres,

To prove : BC = QR

Proof :

In $\triangle$ ABC and $\triangle$ PQR,

$\angle$ BAC= $\angle$ QPR (Given)

AB = PQ (Radii of congruent circle)

AC = PR (Radii of congruent circle)

Thus, $\triangle$ ABC $\cong$ $\triangle$ PQR (By SAS rule)

BC = QR (CPCT)

Benefits of NCERT Solutions for Class 9 Maths Exercise 10.2

The circle is an important part of geometry and there are a lot of applications of circles in whole geometry
Chapter 10 exercise 10.2 in Class 9 Maths presents a wide range of problems that can be based on angle subtended by a chord at a point.
NCERT Class 9 Maths chapter 10 exercise 10.2, will be helpful for the Class 10 chapter 10 circle, as Class 10 chapter 10 circle is an extension of Class 9 Maths chapter 10
NCERT Class 9 Maths chapter 10 exercise 10.2, will be base for the Class 11 chapter 11 conic section
NCERT Class 9 Maths chapter 10 exercise 10.2, will be helpful in JEE Main (joint entrance exam) as the conic section is a major part of the syllabus and the circle is a part of the conic section section

Also, See

NCERT Solutions of Class 10 Subject Wise

Subject Wise NCERT Exemplar Solutions

Frequently Asked Questions (FAQs)

1. How many theorems are covered in NCERT solutions for Class 9 Maths exercise 10.2?

Two theorems are covered through all over exercise 10.2 Class 9 Maths

2. What does CPCT mean using NCERT solutions for Class 9 Maths exercise 10.2?

CPCT means Corresponding parts of congruent triangles

3. What is the definition of a major arc of a circle?

A major arc is a lengthier arc that connects two endpoints on a circle and has a measure larger than 180 degrees.

4. What is a circle's minor arc?

A minor arc is a shorter arc that connects two endpoints on a circle and has a measure of fewer than 180 degrees.

5. What kinds of questions are covered in exercise 10.2 Class 9 Maths?

In questions of exercise 10.2 Class 9 Maths, we have to prove the given statements and they are based on the theorems that are covered before NCERT solutions for Class 9 Maths exercise 10.2

6. How many question are there in exercise 10.2 Class 9 Maths?

There are two questions in exercise 10.2 Class 9 Maths

7. What can you say about the chords if two chords of a circle subtend equal angles at the centre?

If two chords of a circle subtend equal angles at the centre they both are equal.

8. Are angles subtended by chords at the centre are equal?

Yes , angles subtended by chords at the centre are equal

Also Read

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