(A) Let \( P Q \) and \( R S \) be tangents at the extremities of t...

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(A) Let \( P Q \) and \( R S \) be tangents at the extremities of the diameter \( P R \) of a circle of radius \( r \). If \( P S \) and \( R Q \) intersect at a point \( X \) on the circumference of the circle then \( 2 r \) equals:
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[IIT-JEE (Screening) 2001]
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(a) \( \sqrt{P Q \cdot R S} \)
(b) \( \frac{P Q+R S}{2} \)
(c) \( \frac{2 P Q \cdot R S}{P Q+R S} \)
(d) \( \sqrt{\frac{(P Q)^{2}+(R S)^{2}}{2}} \)
(B) Let \( 2 x^{2}+y^{2}-3 x y=0 \) be the equation of a pair of tangents drawn from the origin ' \( O \) ' to a circle of radius 3 with centre in the first quadrant. If \( A \) is one of the points of contact, find the length of \( O A \).
[IIT-JEE (Mains) 2001]
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