Question
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
Given: AB and CD are two equal chords of congruent circles with centres O and O' respectively.
To Prove: ∠AOB = ∠CO'D.
Proof: In ∠OAB and ∠O'CD,
OA = O'C
| Radii of congruent circles
OB = O'D
| Radii of congruent circles
AB = CD | Given
∴ ∆OAB ≅ ∆O'CD | SSS Rule
∴ ∠AOB = ∠CO'D. | C.P.C.T.
