Question 169
The trapezium $ABCD$, where $AB$ and $CD$ are parallel and $AD \lt CD$, is inscribed in the circle $c$. Let $DP$ be a chord of the circle, parallel to $AC$. Assume that the tangent to $c$ at $D$ meets the line $AB$ at $E$ and that $PB$ and $DC$ meet at $Q$. Show that $EQ = AC$.