Question 86
Let $ABCD$ be a trapezoid with $AD \parallel BC$ and $\angle ADC = \angle BAD$, and let $\ell$ be a line not intersecting the line segments $AC$ or $BD$. Assume that $\ell$ intersects the lines $AC, AD, BC, BD$ and $CD$ in the points $P, Q, R, S$ and $T$ respectively. Show that the three circles $\odot(DQT), \odot(BRQ)$ and $\odot(BPS)$ intersect in a common point, where $\odot(XYZ)$ denotes the circumcircle of $XYZ$.