Question

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.

Answer 1

Given: PQ is a diameter of circle which Bisects

Chord AB at C

To prove: PQ bisects ∠AOB

Proof:

In ΔAOC and ΔBOC

OA=OB

OC=OC

AC=BC 

Then Δ AOC ≅ BOC 

∴∠AOC = ∠BOC

Hence PQ bisects ∠AOB