VTMO 2015 — Grade 8 — final Question 4

Acute $ABC$ has $AB \lt AC$, angle bisector $AD$ and median $AM , D , M$ on $BC$. $CH \perp AD$ at $H$; $HM$ meets $AC$ at $N , CH$ meets $AM$ at $E$, and $ED$ meets $AB$ at $F$. Prove $a ) N$ is midpoint $AC$; $b ) DFA$ is isosceles.