Question 14
Let $ABCD$ be a trapezoid such as $(AB)$ and $(CD)$ are parallel. It is assumed that $AD \lt CD$ and $ABCD$ is inscribed in a circle $\Gamma$. Let $P$ on $\Gamma$ such as $(DP)$ is parallel to $(AC)$. The tangent to $\Gamma$ in $D$ cuts $(AB)$ to $E$, and strings $[BP]$ and $[CD]$ intersect in $Q$. Show that $EQ = AC$.