Circles Exercise 5.2 Class 9 Maths NCERT Solutions

The Circles Exercise 5.2 set shows why a chord and the centre always form an isosceles triangle. These NCERT Solutions Class 9 Maths Chapter 5 Circles Exercise 5.2 answers use the simple fact that all radii of a circle are equal. Both questions are short proofs that you write in clear lines.

• Questions solved: both proof questions of Exercise 5.2
• Main skill: using equal radii to prove a triangle is isosceles
• Chapter link: the equal base angles here feed the next chord theorems

These Collegedunia solutions are written by subject teachers, matched to the current 2026-27 Ganita Manjari book, and checked line by line. Each answer stays in plain language, with the reason behind every line spelled out, so a Class 9 student can follow it on the first read.

What Does Class 9 Maths Chapter 5 Circles Exercise 5.2 Cover?

Exercise 5.2 links a chord to the centre. Join the two ends of any chord to the centre and you get a triangle. Two of its sides are radii, so they are equal. That makes the triangle isosceles. The second question extends this to two equal chords, whose triangles turn out to be congruent. The whole set rests on one idea: every radius has the same length. Once you accept that, both proofs become short. You just name the radii, mark them equal, and state the definition you used.

Video Walkthrough

Source: PW Class 9 - NEEV on YouTube

Circles Exercise 5.2 Question Breakdown

The set has two questions, both proofs.

Sample Solved Question from Exercise 5.2

Here is Question 1, written as a short proof.

Question: Show that the triangle formed by a chord and the centre of the circle is isosceles.

Step 1. Let the circle have centre C and let AB be any chord. Join C to A and to B, giving triangle CAB.

Step 2. Points A and B lie on the circle, so CA and CB are radii. Hence CA=r and CB=r.

Step 3. Both sides equal the same radius, so CA=CB.

Final answer. The triangle has two equal sides, so it is isosceles, with the chord AB as its base.

How to Use These Circles Exercise 5.2 Solutions

Collegedunia writes each proof as short, labelled lines with a reason on every step. Follow the answers in this order.

• Name the circle, its centre, and the chord before you begin.
• Mark both radii as r at once, since all radii are equal.
• End with the definition you used, so your proof reads complete.

Work through the questions in order the first time, then use these solutions only to check your own steps. Redoing a question after you read the answer fixes the method far better than reading alone. A short daily set of these problems builds a firm base for the Class 9 annual exam and the circle theorems you meet in the Class 10 syllabus.

More Class 9 Maths Circles Solutions

Open the full chapter or any other exercise of Class 9 Maths Chapter 5 Circles from the table below.