MK-MO 2008 Problem 3

An acute triangle $ABC$ with $AB \neq AC$ is given. Let $V$ and $D$ be the feet of the altitude and angle bisector from $A$ , and let $E$ and $F$ be the intersection points of the circumcircle of $\triangle AVD$ with sides $AC$ and $AB$ , respectively. Prove that $AD$ , $BE$ and $CF$ have a common point.