IMO 1992 LL CAN4

Let p, q, and r be the angles of a triangle, and let a = sin 2p,

imolonglistmathematicsolympiad

IMO 1992 LL CAN4

Origin: CAN

Problem

Let p, q, and r be the angles of a triangle, and let a = sin 2p, b = sin 2q, and c = sin 2r. If s = (a + b + c)/2, show that s(s −a)(s −b)(s −c) \geq0. When does equality hold?