If PA and PB are two tangents to a circle with centre O

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If PA and PB are two tangents to a circle with centre O such that ∠APB = 80°, then, ∠AOP = ?

1. 40°
2. 50°
3. 60°
4. 70°

Correct Option: B

According to question , we draw a figure of a circle with centre O

OA ⊥ PA ; OB ⊥ PB : PA = PB
(tangents from the same external point)
∠APB = 80° : OA = OB = radius

∴ ∠APO =	80°	= 40°
	2

∴ ∠AOP = 90° – 40° = 50°.