RMO 2012 A5

Let $ABC$ be a triangle. Let $BE$ and $CF$ be internal angle bisectors of $\angle B$ and $\angle C$ respectively with $E$ on $AC$ and $F$ on $AB$ . Suppose $X$ is a point on the segment $CF$ such that $AX$ perpendicular $CF$ ; and $Y$ is a point on the segment $BE$ such that $AY$ perpendicular $BE$ . Prove that $XY = (b + c-a)/2$ where $BC = a, CA = b$ and $AB = c$ .