KURSCHAK 1961 Problem 3

Two circles centers $O$ and $O'$ are disjoint. $PP'$ is an outer tangent (with $P$ on the circle center O, and P' on the circle center $O'$ ). Similarly, $QQ'$ is an inner tangent (with $Q$ on the circle center $O$ , and $Q'$ on the circle center $O'$ ). Show that the lines $PQ$ and $P'Q'$ meet on the line $OO'$ .