Quantitative Aptitude Ques 1730

Question: In the given figure, O is the centre of a circle, PQL and PRM axe the tangents at the points Q and R, respectively and S is a point on the circle such that $ \angle SQL=50{}^\circ $ and $ \angle SRM=60{}^\circ . $ Then, $ \angle QSR $ is equal to

Options:

A) $ 40{}^\circ $

B) $ 50{}^\circ $

C) $ 60{}^\circ $

D) $ 70{}^\circ $

Show Answer

Answer:

Correct Answer: D

Solution:

  • Since, $ PQL $ is a tangent and $ OQ $ is a radius, so $ \angle OQL=90{}^\circ $ $ \angle OQS=(90{}^\circ -50{}^\circ )=40{}^\circ $ Now, $ OQ=OS $

$ \Rightarrow $ $ \angle OSQ=\angle OQS=40{}^\circ $ Similarly, $ \angle ORQ=(90{}^\circ -60{}^\circ )=30{}^\circ $ and $ OR=OS $

$ \Rightarrow $ $ \angle OSR=\angle ORS=30{}^\circ $

$ \Rightarrow $ $ \angle QSR=\angle OSQ+\angle OSR $ $ =(40{}^\circ +30{}^\circ )=70{}^\circ $

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