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Geometric inequality with angles

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September 1, 2010
trigonometrygeometryarea of a trianglegeometric inequalityIMO ShortlistIMO Longlist

Problem Statement

Let p,qp, q, and rr be the angles of a triangle, and let a=sin⁡2p,b=sin⁡2qa = \sin2p, b = \sin2q, and c=sin⁡2rc = \sin2r. If s=(a+b+c)2s = \frac{(a + b + c)}2, show that s(s−a)(s−b)(s−c)≥0.s(s - a)(s - b)(s -c) \geq 0. When does equality hold?
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