China Western Mathematical Olympiad

$AB$ is a diameter of the circle $O$, the point $C$ lies on the extended line $AB$ produced. A line passing through $C$ intersects with the circle $O$ at points $D$ and $E$. $OF$ is a diameter of the circumcircle $O_1$ of $△BOD$. Join $CF$ and its extension, which intersects the circle $O_1$ at $G$. Prove that points $O$, $A$, $E$, $G$ are concyclic.