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Question

In the given figure, O is the centre of a circle; PQL and PRM are the tangents at the points Q and R respectively, and S is a point on the circle, such that ∠SQL = 50° and ∠SRM = 60°. Find ∠QSR.


(a) 40°
(b) 50°
(c) 60°
(d) 70°

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Solution

(d) 70°PQL is a tangent OQ is the radius; so, OQL=900. OQS=900-500=400Now, OQ=OS (Radius of the same circle)OSQ=OQS=400Similarly, ORS=900-600=300,And ,OR=OS (Radius of the same circle)OSR=ORS=300QSR=OSQ+OSRQSR=400+300QSR=700

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