Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centers.

Given : Two congruent circles with centres O and O’ and radii r, which have chords PQ and RS respectively such that PQ = RS.

Proof: In ∆POQ and ∆RO’S, we have
PQ = RS [Given]
OP = O’R [Each equal to r]

OQ = O’S [Each equal to r]
∴ ∆POQ ≅ ∆RO’S [By SSS congruence]
⇒ ∠POQ = ∠RO’S [C.P.C.T.]