IMO 1992 LL POR58

Let ABC be a triangle. Denote by a, b, and c the lengths of

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IMO 1992 LL POR58

Origin: POR

Problem

Let ABC be a triangle. Denote by a, b, and c the lengths of the sides opposite to the angles A, B, and C, respectively. Prove that7 bc a + b + c = sin A + sin B + sin C cos(A/2) sin(B/2) sin(C/2).