IMO 2006 Shortlist G2

Let ABCD be a trapezoid with parallel sides AB > CD. Points K and L lie on the line segments AB and CD, respectively, so...

IMO 2006 Shortlist G2

Category: Geometry

Problem

Let ABCD be a trapezoid with parallel sides AB > CD. Points K and L lie on the line segments AB and CD, respectively, so that AK/KB = DL/LC. Suppose that there are points P and Q on the line segment KL satisfying ∠APB = ∠BCD and ∠CQD = ∠ABC. Prove that the points P, Q, B and C are concyclic. (Ukraine)