NCERT Solutions for Class 9 Maths Exercise 10.2 Chapter 10 Circles

*According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 9.

NCERT Solutions for Class 9 Maths Chapter 10 – Circles Exercise 10.2 are provided here for students to prepare thoroughly for the annual exam. These solutions are designed by the subject-matter experts at BYJU’S according to the Class 9 NCERT syllabus and guidelines (2023-24) as prescribed by the CBSE. These NCERT Solutions for Class 9 Maths are helpful for students to do their homework assigned in schools and also score good marks in the annual exam.

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

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Access Other Exercise Solutions of Class 9 Maths Chapter 10 – Circles

Exercise 10.1 Solutions 2 Questions (2 Short)

Exercise 10.3 Solutions 3 Questions (3 long)

Exercise 10.4 Solutions 6 Questions (6 long)

Exercise 10.5 Solutions 12 Questions (12 long)

Exercise 10.6 Solutions 10 Questions (10 long)

Access Answers to NCERT Class 9 Maths Chapter 10 – Circles Exercise 10.2

1. 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.

Solution:

To recall, a circle is a collection of points whose every point is equidistant from its centre. So, two circles can be congruent only when the distance of every point of both circles is equal from the centre.

In the second part of the question, it is given that AB = CD, i.e. two equal chords.

Now, it is to be proven that angle AOB is equal to angle COD.

Proof:

Consider the triangles ΔAOB and ΔCOD,

OA = OC and OB = OD (Since they are the radii of the circle)

AB = CD (As given in the question)

So, by SSS congruency, ΔAOB ≅ ΔCOD

∴ By CPCT, we get

∠AOB = ∠COD. Hence proved.

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

Solution:

Consider the following diagram:

Here, it is given that ∠AOB = ∠COD, i.e. they are equal angles.

Now, we will have to prove that the line segments AB and CD are equal, i.e. AB = CD.

Proof:

In triangles AOB and COD,

∠AOB = ∠COD (as given in the question)

OA = OC and OB = OD (these are the radii of the circle)

So, by SAS congruency, ΔAOB ≅ ΔCOD.

∴ By the rule of CPCT, we get

AB = CD. Hence proved.

Exercise 10.2 consists of two questions based on two theorems, which were explained before this exercise. They are as follows:

Theorem 1: Equal chords of a circle subtend equal angles at the centre.

Theorem 2: If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.

Students have to prove the given scenarios with respect to the above-given theorems. To help them, we have given a detailed explanation for each question in the NCERT Solutions for Class 9 Maths Chapter 10.

The questions in Exercise 10.2 have mid-length answers, which students can easily grasp. Solve NCERT Solutions where problems are resolved in a comprehensive way following each and every step.