IMO Shortlist 1959 problem 6
Two planes,
and
, intersect along the line
. The point
is given in the plane
, and the point
in the plane
; neither of these points lies on the straight line
. Construct an isosceles trapezoid
(with
) in which a circle can be inscribed, and with vertices
and
lying in planes
and
respectively.
%V0
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.
Source: Međunarodna matematička olimpijada, shortlist 1959
Školjka 
