ILL 1983 Problem 62

$A$ circle $\gamma$ is drawn and let $AB$ be a diameter. The point $C$ on $\gamma$ is the midpoint of the line segment $BD$ . The line segments $AC$ and $DO$ , where $O$ is the center of $\gamma$ , intersect at $P$ . Prove that there is a point $E$ on $AB$ such that $P$ is on the circle with diameter $AE.$