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AP EAMCET202018 Sep 2020Morning ShiftMathematicsCircleActual

Let (P Q ) and (R S ) be tangents at the extremities of a diameter (P R ) of a circle of radius (r ) such that (P S ) and (R Q ) intersect at a point (X ) on the circumference of the circle, then (2 r ) equals

Options

  1. A( P Q R S )
  2. B( P Q+R S 2 )
  3. C( 2 P Q R S P Q+R S )
  4. D( (P Q)^2+(R S)^2 2 )

Correct answer

A. ( P Q R S )

Step-by-step solution

According to the question, from the diagram, in ( P Q R ) ( = P Q P R P R=P Q )...(i) and in ( P R S ), ( aligned & (90^ - ) = R S P R P R=R S (i) & P Q =R S & = P Q R S (ii) aligned ) From Eqs. (ii) and (iii), we have ( aligned P R & =R S P Q R S = P Q R S 2 r & = P Q R S P R=2 r aligned )

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