CZ-SK-MO 2011 Problem 5

In acute triangle ABC, which is not equilateral, let $P$ denote the foot of the altitude from $C$ to side $AB$ ; let $H$ denote the orthocenter; let $O$ denote the circumcenter; let $D$ denote the intersection of line $CO$ with $AB$ ; and let $E$ denote the midpoint of $CD$ . Prove that line $EP$ passes through the midpoint of $OH$ .