CWMO 2002 Problem 2

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 $ABC$ .