RS-SMO 2014 Problem 2

On sides $BC$ and $AC$ of $\triangle ABC$ given are $D$ and $E$ , respectively. Let $F$ ( $F \neq C$ ) be a point of intersection of circumcircle of $\triangle CED$ and line that is parallel to $AB$ and passing through C. Let $G$ be a point of intersection of line $FD$ and side $AB$ , and let $H$ be on line $AB$ such that $\angle HDA = \angle GEB$ and $H-A-B$ . If $DG=EH$ , prove that point of intersection of $AD$ and $BE$ lie on angle bisector of $\angle ACB$ .

Proposed by Milos Milosavljevic