MathDB

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 \angle{APB} \equal{} \angle{BCD}\qquad\text{and}\qquad \angle{CQD} \equal{} \angle{ABC}. Prove that the points

P

Q

B

and

C

are concyclic.
Proposed by Vyacheslev Yasinskiy, Ukraine

Problem Statement