Question 184
Let $ABCD$ be a trapezium with the bottom edge $BC$ ($BC \parallel AD$ and $BC \gt AD$) and inscribed in the circle $(O)$ ($O$ is the center of $(O)$). Let $P$ be a point moving on the line $BC$ outside the segment $BC$ such that $PA$ doesn't touch the circle $(O)$. The circle with the diameter $PD$ intersects $(O)$ in $E$ ($E \neq D$). Let $M$ be the point of intersection of $BC$ and $DE$, and $N$ ($N \neq A$) be the second point of intersection of $PA$ and $(O)$. Prove that the line $MN$ passes through a fixed point.