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KVPY2012MathematicsCircle

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 RQS equals -

Options

  1. A86^
  2. B87^
  3. C88^
  4. D89^

Correct answer

D. 89^

Step-by-step solution

Ry Cosine rule array l ( QS )²=2-2 2^ QS =2 1^ array Now by sine rule in RQS array l = 2^ 2 1^ =89^ RQS =180^ - (2^ +89^ )=180^ -91^ =89^ array

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