BALKAN 2003 Problem 2

Let $ABC$ be a triangle, and let the tangent to the circumcircle of the triangle $ABC$ at $A$ meet the line $BC$ at $D$ . The perpendicular to $BC$ at $B$ meets the perpendicular bisector of $AB$ at $E$ . The perpendicular to $BC$ at $C$ meets the perpendicular bisector of $AC$ at $F$ . Prove that the points $D$ , $E$ and $F$ are collinear.

Valentin Vornicu