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Inequality involving the tangent of an angle

Source: Poland Math Olympiad 1995 Round 1 #5

June 12, 2023
trigonometryinequalities

Problem Statement

Given triangle ABCABC in the plane such that ∠CAB=a>π/2\angle CAB = a > \pi/2. Let PQPQ be a segment whose midpoint is the point AA. Prove that (BP+CQ)tan⁡a/2≥BC(BP+CQ) \tan a/2 \geq BC.
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