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Question

If PA and PB are two tangents to a circle with centre O, such that ∠AOB = 110°, find ∠APB.


(a) 55°
(b) 60°
(c) 70°
(d) 90°

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Solution

(c) 70°
Given, PA and PB are tangents to a circle with centre O, withAOB=1100.Now, we know that tangents drawn from an external point are perpendicularto the radius at the point of contact.So, OAP=900 andOBP=900.OAP+OBP=900+900=1800, which shows that OABP is a cyclicquadrilateral.AOB+APB=18001100+APB=1800APB=1800-1100APB=700

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