Question 119
Let triangle $ABC$ be acute-angled and inscribed in a circle $\omega$. Let $M$ be the midpoint of arc $BC$ that does not contain point $A$. Let point $D$ be chosen on segment $AM$ such that $D$ lies inside triangle $ABC$. Line $BD$ intersects side $AC$ at point $N$, and intersects the circle $\omega$ again at point $P$. On segment $AN$, choose point $E$ such that $\angle NDE = \angle CAM$. Let line $DE$ intersect side $BC$ at point $F$. Let $L$ be the second intersection point of $\omega$ with the line through $M$ that is parallel to line $BP$. Prove that the lines $EP$, $DL$, and $FM$ are concurrent.
(Khulan Tumenbayar)
(Khulan Tumenbayar)