**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:**

We have two congruent circles with centres O and O' respectively. They are congruent which means that they have same radii.

It is also given that

We need to prove that they subtend equal angles at their centres. In other words, we need to prove that

In and , we have

**(Congruent circles have same radii)**

** (Given)**

**(Congruent circles have same radii)**

Therefore, **by SSS congruence rule**, we have .

**(Corresponding parts of congruent triangles are equal.)**

**It means that equal chords of congruent circles subtend equal angles at their centres.**