# 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:**

Let QR and YZ be the equal chords of 2 congruent circles.

Then, QR = YZ

We need to prove that they subtend equal angles at the center. That is, ∠QPR = ∠YXZ

We know that the radii of both circles are equal. So, we get: PR = PQ = XZ = XY

Consider the 2 triangles, ∆PQR and ∆XYZ.

PQ = XY (Radii are equal)

PR = XZ (Radii are equal)

QR = YZ (Chords are equal)

By SSS congruency, ∆PQR is congruent to ∆XYZ.

So, by CPCT (Corresponding parts of congruent triangles), we get ∠QPR =∠YXZ.

Hence, proved that equal chords of congruent circles subtend equal angles at their centers.

**Video Solution:**

## 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.

### Maths NCERT Solutions Class 9 - Chapter 10 Exercise 10.2 Question 1:

**Summary:**

If two circles are congruent, they have the same radii, then equal chords of congruent circles subtend equal angles at their centers