Question 70
Consider the isosceles triangle $ABC$ with $AB = AC$. A semicircle of diameter $EF$ situated on the side $BC$, is tangent to the sides $AB$ and $AC$ at $M$ and $N$, respectively. The line $AE$ intersects the semicircle at $P$. Prove that the line $PF$ passes through the midpoint of the chord $MN$.