CGMO 2004 Problem 6

Given an acute triangle $ABC$ with $O$ as its circumcenter. Line $AO$ intersects $BC$ at $D$ . Points $E$ , $F$ are on $AB$ , $AC$ respectively such that $A$ , $E$ , $D$ , $F$ are concyclic. Prove that the length of the projection of line segment $EF$ on side $BC$ does not depend on the positions of $E$ and $F$ .