FKMO 2010 Problem 2

Let $I$ be the incentre and $O$ the circumcentre of a given acute triangle $ABC$ . The incircle is tangent to $BC$ at $D$ . Assume that $\angle B < \angle C$ and the segments $AO$ and $HD$ are parallel, where $H$ is the orthocentre of triangle $ABC$ . Let the intersection of the line $OD$ and $AH$ be $E$ . If the midpoint of $CI$ is $F$ , prove that $E,F,I,O$ are concyclic.