CWMO 2006 Problem 6

$AB$ is a diameter of the circle $O$ , the point $C$ lies on the line $AB$ produced. A line passing though $C$ intersects with the circle $O$ at the point $D$ and $E$ . $OF$ is a diameter of circumcircle $O_{1}$ of $\triangle BOD$ . Join $CF$ and produce, cutting the circle $O_{1}$ at $G$ . Prove that points $O,A,E,G$ are concyclic.