INMO 1998 Problem 1

In a circle $C_1$ with centre $O$ , let $AB$ be a chord that is not a diameter. Let $M$ be the midpoint of this chord $AB$ . Take a point $T$ on the circle $C_2$ with $OM$ as diameter. Let the tangent to $C_2$ at $T$ meet $C_1$ at $P$ . Show that $PA^2 + PB^2 = 4 \cdot PT^2$ .