Question 35
Let $\triangle ABC$ be a triangle inscribed in a circle $(O)$. The point $P$ is an arbitrary point on interior angle bisector $AD$ of triangle $ABC$, $D$ belongs to segment $BC$ and $P$ lies between $A$ and $D$. The line $BP$ meets segment $AC$ at $E$, the line $CP$ meets segment $AB$ at $F$. The projection of $P$ on segment $BC$ is $M$. Suppose that two lines $PM, EF$ intersect at $N$ and $AN$ meets $OP$ at $L$. Prove that the line $ML$ always passes through a certain fixed point when $P$ is moving on $AD$.