APMO 1998 - Asian Pacific Mathematics Olympiad Question 4

Let $ABC$ be a triangle and $D$ the foot of the altitude from $A$. Let $E,F$ lie on a line through $D$, with $AE\perp BE$, $AF\perp CF$, and $E,F\ne D$. Let $M,N$ be the midpoints of $BC,EF$, respectively. Prove that $AN\perp NM$.