Prove that a diameter of a circle which bisects a chord of the circle also bisects the angle subtended by the chord at the centre of the circle.

Question

Philoid · Accepted Answer

Given that,

PQ is a diameter of circle which bisects chord AB to C

To prove: PQ bisects ∠AOB

Proof: In ,

OA = OB (Radius of circle)

OC = OC (Common)

AC = BC (Given)

Then,

(By SSS congruence rule)

∠AOC = ∠BOC (By c.p.c.t)

Hence, PQ bisects ∠AOB.