Problem

Source: China Western Mathematical Olympiad 2002 P2

Tags: geometry, parallelogram, circumcircle, geometry proposed



Let O be the circumcenter of acute triangle ABC. Point P is in the interior of triangle AOB. Let D,E,F be the projections of P on the sides BC,CA,AB, respectively. Prove that the parallelogram consisting of FE and FD as its adjacent sides lies inside triangle ABC.