Question 200
Let $ABCD$ be a trapezoid with parallel sides $AB \gt CD$. 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
$$
\angle APB = \angle BCD \quad \text{and} \quad \angle CQD = \angle ABC.
$$
Prove that the points $P$, $Q$, $B$ and $C$ are concyclic.
$$
\angle APB = \angle BCD \quad \text{and} \quad \angle CQD = \angle ABC.
$$
Prove that the points $P$, $Q$, $B$ and $C$ are concyclic.