Question 3
Let $ABC$ be an acute triangle with $AB\lt AC$. Its angle bisector is $AD$ and its median is $AM$, where $D,M\in BC$. From $C$, draw the perpendicular to $AD$ meeting it at $H$. The line $HM$ meets $AC$ at $N$; $CH$ meets $AM$ at $E$; and $ED$ meets $AB$ at $F$.
a) Prove that $N$ is the midpoint of $AC$.
b) Prove that triangle $DFA$ is isosceles.
a) Prove that $N$ is the midpoint of $AC$.
b) Prove that triangle $DFA$ is isosceles.