SATHEE: Quantitative Aptitude Ques 2325

Quantitative Aptitude Ques 2325

Question: P and Q are two points on a circle with centre at O. R is a point on the minor arc of the circle between the points P and Q. The tangents to the circle at the points P and Q meet each other at the point S. If $ \angle PSQ=20{}^\circ , $ then $ \angle PRQ $ is equal to

Options:

A) $ 200{}^\circ $

B) $ 160{}^\circ $

C) $ 100{}^\circ $

D) $ 80{}^\circ $

Show Answer

Answer:

Correct Answer: C

Solution:

Join P and Q with an another point, say T, on the major arc. Also, join PO and QO. In POQS, $ \angle PSQ=20{}^\circ $ $ \angle OPS=\angle OQS=90{}^\circ $ [ $ \because $ Tangent] $ \angle POQ=360{}^\circ -(90{}^\circ +90{}^\circ +20{}^\circ )=160{}^\circ $

$ \therefore $ $ \angle PTQ=\frac{1}{2}\angle POQ=\frac{1}{2}\times 160{}^\circ =80{}^\circ $ Now, PTQR is a cyclic quadrilateral. $ \angle PRQ=180{}^\circ -\angle PTQ $ $ =180{}^\circ -80{}^\circ =100{}^\circ $

Quantitative Aptitude Ques 2324

Quantitative Aptitude Ques 2326

Quantitative Aptitude Ques 2325

Question: P and Q are two points on a circle with centre at O. R is a point on the minor arc of the circle between the points P and Q. The tangents to the circle at the points P and Q meet each other at the point S. If $ \angle PSQ=20{}^\circ , $ then $ \angle PRQ $ is equal to

Options:

Answer:

Solution:

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