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Question

In the given figure, O is the centre of a circle, PQ is a chord and the tangent PT at P makes an angle of 50° with PQ. Then, ∠POQ = ?


(a) 130°
(b) 100°
(c) 90°
(d) 75°

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Solution

(b) 100°Given,∠QPT=500Now,∠OPT=900 (Since tangents drawn from an external point areperpendicular to the radius at point of contact)∠OPQ=∠OPT-∠QPT=900-500=400OP=OQRadii of the same circle∠OPQ=∠OQP=400InPOQ,POQ+OPQ+∠OQP=1800POQ+400+400=1800POQ=1800-400+400∠POQ=1800-800∠POQ=1000

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