KöMaL 2016 B4823

In an acute-angled triangle $ABC$ ($AB < AC$), the foot of the altitude from vertex $A$ is $D$, and the centre of the circumscribed circle is $O$. Prove that if the exterior angle bisector of $BAC\sphericalangle$ is parallel to $OD$, then the diagonals of the quadrilateral $AODC$ are equal.