Question 6
Let trapezoid $ABCD$, with larger base $BC$, be inscribed in circle $(O)$ with center $O$. A point $P$ varies on the line $BC$, outside segment $BC$, such that $PA$ is not tangent to $(O)$. The circle with diameter $PD$ meets $(O)$ again at $E$ ($E\ne D$). Let $M=BC\cap DE$, and let $N$ be the intersection of $PA$ with $(O)$ other than $A$. Prove that $MN$ passes through a fixed point.