IMO 1989 LL MOR72

Origin: MOR

Problem

Let ABCD be a quadrilateral inscribed in a circle with diam- eter AB such that BC = a, CD = 2a, DA = 3 \sqrt 5−1 a. For each point M on the semicircle AB not containing C and D, denote by h1, h2, h3 the distances from M to the sides BC, CD, and DA. Find the maximum of h1 + h2 + h3.