KVPY SA Exam 2012 Question Paper

Question : 10 of 80

Marks: +1, -0

Suppose Q is a point on the circle with centre P and radius 1, as shown in the figure; R is a point outside the circle such that QR = 1 and ∠QRP = 2°. Let S be the point where the segment RP intersects the given circle. Then measure of ∠ROS equals

86°
87°
88°
89°

Validate

Solution:

By Cosine rule

(QS) ^2= 2- 2\cos 2º

QS =2\sin1º

Now by sine rule in ∆RQS

\sinθ={\sin 2°}/{2\sin 1°}

θ=89°

∠ RQS = 180º – (2º +89º) = 180º – 91º = 89º

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