AT-OEMO-FED1 2016 Problem 2

We are given an acute triangle $ABC$ with $AB > AC$ and orthocenter $H$ . The point $E$ lies symmetric to $C$ with respect to the altitude $AH$ . Let $F$ be the intersection of the lines $EH$ and $AC$ . Prove that the circumcenter of the triangle $AEF$ lies on the line $AB$ .

(Karl Czakler)