## The fixed point

Let $ABC$ be a triangle inscribed the circle $(O)$ and $A'$ is a fixed point on $(O)$. $P$ moves on $BC$, $K$ belongs to $AC$ so that $PK$ is always parallel to a fixed line $d$. The circumcircle of triangle $APK$ cuts the circle $(O)$ at a second point $E$. $AE$ cuts $BC$ at $M$. $A'P$ cuts the circle $(O)$ at a second point $N$. Prove that the line $MN$ passes through a fixed point.