SMO 2005 Problem 2

Let $G$ be the centroid of triangle $ABC$ . Through $G$ draw a line parallel to $BC$ and intersecting the sides $AB$ and $AC$ at $P$ and $Q$ respectively. Let $BQ$ intersect $GC$ at $E$ and $CP$ intersect $GB$ at $F$ . If $D$ is midpoint of $BC$ , prove that triangles $ABC$ and $DEF$ are similar