Question 18
Let $ABCD$ be a trapezoid with $AB \parallel CD$ and $AB \gt CD$. The points $K$ and $L$ lie on the sides $AB$ and $CD$ respectively with $\dfrac{AK}{KB} = \dfrac{DL}{LC}$. The points $P$ and $Q$ lie on the segment $KL$ such that
$$
\angle APB = \angle BCD \quad \text{and} \quad \angle CQD = \angle ABC
$$
Show that the points $P$, $Q$, $B$ and $C$ lie on a circle.
$$
\angle APB = \angle BCD \quad \text{and} \quad \angle CQD = \angle ABC
$$
Show that the points $P$, $Q$, $B$ and $C$ lie on a circle.