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

Question

Philoid · Accepted Answer

Let us consider two congruent circles (circles of same radius) with centers 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 (SSS congruence rule)

AB = CD (By CPCT)

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