Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle then 2r equals

JEE Advanced Mathematics question

Let and be tangents at the extremities of the diameter of a circle of radius . If and intersect at a point on the circumference of the circle then equals

(A)Correct
(B)
(C)
(D)

Answer: (A)

Solution

*(Figure in book: R(−r, 0), P(r, 0) ends of the diameter; tangents at P and R are vertical; Q(r, λ) on the tangent at P, S(−r, μ) on the tangent at R; PS and RQ meet at X on the circle with a right angle at X.)*

Let , . Since lies on the circle with diameter , , so

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Question ID VK-110565