Prove that equal chords of congruent circles subtend equal angles at their centers.

We know that,

Congruent circles have equal radius.

Let there be two congruent circles with center O and O' and radius equal to r units.

Let there be two equal chords AB and CD.

In △ AOB and △ CO'D,

⇒ OA = O'C (Both equal to r units)

⇒ OB = O'D (Both equal to r units)

⇒ AB = CD (Given)

⇒ △ AOB ≅ △ CO'D (By S.S.S. axiom)

We know that,

Corresponding parts of congruent triangles are equal.

∴ ∠AOB = ∠CO'D.

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