2nd Iberoamerican Mathematical Olympiad Problems 1987

A1.  Find f(x) such that f(x)2f( (1-x)/(1+x) ) = 64x for x not 0, ±1. A2.  In the triangle ABC, the midpoints of AC and AB are M and N respectively. BM and CN meet at P. Show that if it is possible to inscribe a circle in the quadrilateral AMPN (touching every side), then ABC is isosceles.