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 ΔAOB and ΔCO'D,

∠AOB = ∠CO'D (Given)

OA = O'C (Radii of congruent circles)

OB = O'D (Radii of congruent circles)

∴ ΔAOB ≅ ΔCO'D (SAS congruence rule)

⇒ AB = CD (By CPCT)

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