The tangents at two points A and B on the circle with centre

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The tangents at two points A and B on the circle with centre O intersects at P ; If in quadrilateral PAOB, ∠AOB: ∠APB = 5 : 1, then measure of ∠APB is :

1. 30°
2. 60°
3. 45°
4. 15°

Correct Option: A

As per the given in question , we draw a figure of a circle with centre O,

Given that , ∠AOB: ∠APB = 5 : 1,
From figure ,
∠ OAP = ∠ OBP = 90°
∠ AOB + ∠ APB = 180°
⇒ 5∠ APB + ∠ APB = 180°
⇒ 6 ∠ APB = 180°
⇒ ∠ APB = 30°