PL-OM 1989 Problem 2

$k_1, k_2, k_3$ are three circles. $k_2$ and $k_3$ touch externally at $P$ , $k_3$ and $k_1$ touch externally at $Q$ , and $k_1$ and $k_2$ touch externally at $R$ . The line $PQ$ meets $k_1$ again at $S$ , the line $PR$ meets $k_1$ again at $T$ . The line $RS$ meets $k_2$ again at $U$ , and the line $QT$ meets $k_3$ again at $V$ . Show that $P, U, V$ are collinear.