PAMO 2008 Problem 2

Let $C_1$ be a circle with centre $O$ , and let $AB$ be a chord of the circle that is not a diameter. $M$ is the midpoint of $AB$ . Consider a point $T$ on the circle $C_2$ with diameter $OM$ . The tangent to $C_2$ at the point $T$ intersects $C_1$ at two points. Let $P$ be one of these points. Show that $PA^2+PB^2=4PT^2$ .