Question

Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

Answer 1

Let us consider two congruent circles (circles of same radius) with centres as O and O'.

In ∆AOB and ∆CO'D, 

∠AOB = ∠CO'D (Given) 

OA = O'C (Radii of congruent circles) 

OB = O'D (Radii of congruent circles) 

∠∆AOB ∠∆CO'D (SSS congruence rule) 

⇒ AB = CD (By CPCT) 

Hence, if chords of congruent circles subtend equal angles at their centres, then the chords are equal.