Question

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

Answer 1

Given: AB and CD are two equal chords of a congruent circle with centres O and O respectively.

To prove: ∠AOB = ∠CO'D

Proof:
In ΔOAB and ΔO'CD
OA = O'C                            ...[ ∵ Radii of congruent circles ]
OB = O'D                            ...[ ∵ Radii of congruent circles ]
AB = CD                              ...[ Given ] 
ΔOAB ≅ ΔO'CD                   ...[ By SSS congruence criterion ]
∠AOB = ∠CO'D                   ...[ c. p. c. t ]