PL-OM 1991 Problem 5

Two noncongruent circles $k_1$ and $k_2$ are exterior to each other. Their common tangents intersect the line through their centers at points $A$ and $B$ . Let $P$ be any point of $k_1$ . Prove that there is a diameter of $k_2$ with one endpoint on line $PA$ and the other on $PB$ .