RMO 2018 K1

Let $ABC$ be an acute angled triangle and let $D$ be an interior point of the segment $BC$ . Let the circumcircle of $ACD$ intersect $AB$ at $E$ ( $E$ between $A$ and $B$ ) and let circumcircle of $ABD$ intersect $AC$ at $F$ ( $F$ between $A$ and $C$ ). Let $O$ be the circumcenter of $AEF$ . Prove that $OD$ bisects $\angle EDF$ .