IMO 1959 Problem 6

Two planes, $P$ and $Q$ , intersect along the line $p$ . The point $A$ is given in the plane $P$ , and the point $C$ in the plane $Q$ ; neither of these points lies on the straight line $p$ . Construct an isosceles trapezoid $ABCD$ (with $AB \parallel CD$ ) in which a circle can be inscribed, and with vertices $B$ and $D$ lying in planes $P$ and $Q$ respectively.