Let be a trapezoid with parallel sides . Points and lie on the line segments and , respectively, so that . Suppose that there are points and on the line segment satisfying and . Prove that the points , , and are concylic.
%V0
Let $ABC$ be a trapezoid with parallel sides $AB > CD$. Points $K$ and $L$ lie on the line segments $AB$ and $CD$, respectively, so that $\frac {AK}{KB} = \frac {DL}{LC}$. Suppose that there are points $P$ and $Q$ on the line segment $KL$ satisfying $\angle{APB} = \angle{BCD}$ and $\angle{CQD} = \angle{ABC}$. Prove that the points $P$, $Q$, $B$ and $C$ are concylic.
Izvor: Međunarodna matematička olimpijada, shortlist 2006
Školjka 
be a trapezoid with parallel sides 
. Points 
and 
lie on the line segments 
and 
, respectively, so that 
. Suppose that there are points 
and 
on the line segment 
satisfying 
and 
. Prove that the points 
and 
are concylic.