MathNet 2008-part-02 — 165 problems (EN–VI) Question 155

Let $ABC$ be an isosceles triangle with $\overline{AB} = \overline{AC}$. Let $D$ be the midpoint of $BC$, $M$ the midpoint of $AD$ and $N$ the projection of $D$ to $BM$. Prove that $\angle ANC = 90^\circ$.