Theorem 10.2 : If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal Class 9

Given: In ∆AOB and ∆POQ, ∠AOB = ∠POQ.

To prove: Length of chord AB=PQ.

Proof: In ∆AOB and ∆POQ

⇒ AB = PQ (Given) ……..(1)

⇒ OA = OB= OP=OQ (Radii of the circle) ……..(2)

From eq 1 and 2, we get;

⇒ ∆AOB ≅ ∆POQ (SSS congruence)

Therefore, by C.P.C.T. (corresponding parts of congruent triangles), we get;

⇒ ∠AOB = ∠POQ

Hence, Proved.