OMM 2005 Problem 6

Let $ABC$ be a triangle and $AD$ be the angle bisector of $<BAC$ , with $D$ on $BC$ . Let $E$ be a point on segment $BC$ such that $BD = EC$ . Through $E$ draw $l$ a parallel line to $AD$ and let $P$ be a point in $l$ inside the triangle. Let $G$ be the point where $BP$ intersects $AC$ and $F$ be the point where $CP$ intersects $AB$ . Show $BF = CG$ .