NL-NWO 2007 Problem 5

A triangle $ABC$ and a point $P$ inside this triangle are given. Define $D, E$ and $F$ as the midpoints of $AP, BP$ and $CP$ , respectively. Furthermore, let $R$ be the intersection of $AE$ and $BD, S$ the intersection of $BF$ and $CE$ , and $T$ the intersection of $CD$ and $AF$ . Prove that the area of hexagon $DRESFT$ is independent of the position of $P$ inside the triangle.