Question 100
Given is $\triangle ABC$ with circumcircle $\Gamma$. Let $M$ be the midpoint of the arc $BC$ of $\Gamma$ not containing $A$. The vertex $N$ on $\Gamma$ is the antipode of $A$. The line through $B$ perpendicular to $AM$ intersects $AM$ at $D$ and intersects $\Gamma$ a second time at $P \neq B$. The line through $D$ perpendicular to $AC$ intersects $AC$ at the vertex $E$ and intersects $BC$ at the vertex $F$.
Prove that $ND$, $MF$ and $PE$ are concurrent.
Prove that $ND$, $MF$ and $PE$ are concurrent.