**Given: **A circle with center ‘O’. Having points P and Q subtends angles ∠PAQ and ∠PBQ at points A and B.

**To Prove: **∠PAQ = ∠PBQ

**Proof:** From Theorem 10.8: Angle subtended by an arc at the center is double the angle subtended by it at any other point on the circle.

Therefore, ∠POQ = 2∠PAQ ….(i)

and, ∠POQ = 2∠PBQ ….(ii)

from eq(i) and (ii), we get

2∠PBQ = 2∠PAQ

∠PBQ = ∠PAQ

Hence,Proved.

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