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.

Let, there be two circles with center P and X with equal radius.

From figure,

QR and YZ are equal chords.

In ∆ PQR and ∆ XYZ,

⇒ PQ = XY (Radius of congruent circles)

⇒ PR = XZ (Radius of congruent circles)

⇒ QR = YZ (Chords are equal)

∴ ∆ PQR ≅ ∆ XYZ (By S.S.S. congruence rule)

We know that,

Corresponding parts of congruent triangles are equal.

⇒ ∠QPR = ∠YXZ (By C.P.C.T.)

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