Q7 of 100 Page 16

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.

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.


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