Data : Two circles having centres O and O’ and having equal radius.
Chord AB = CD.
To Prove: Equal chords of congruent circles subtend equal angles at their centres.
Or ∠AOB = ∠CO’D
Proof: In ∆AOB and ∆CO’D,
OA = O’C (Data)
OB = O’D (Data)
AB = CD (Data)
∴ ∆AOB ≅ ∆CO’D
∴ ∠AOB = ∠CO’D.