AUSTRIAN-POLISH 1997 Problem 1

Let $P$ be the intersection of lines $l_1$ and $l_2$ . Let $S_1$ and $S_2$ be two circles externally tangent at $P$ and both tangent to $l_1$ , and let $T_1$ and $T_2$ be two circles externally tangent at $P$ and both tangent to $l_2$ . Let $A$ be the second intersection of $S_1$ and $T_1, B$ that of $S_1$ and $T_2, C$ that of $S_2$ and $T_1$ , and $D$ that of $S_2$ and $T_2$ . Show that the points $A,B,C,D$ are concyclic if and only if $l_1$ and $l_2$ are perpendicular.