Question 41
Let $\triangle ABC$ be an isosceles triangle with $\angle BAC \gt 90^\circ$, and let $C$ be the circle centered at $A$ with radius $AB$. Let $M$ be the midpoint of side $AC$. The line $BM$ intersects the circle $C$ a second time at point $D$. Let $E$ be a point on the circle $C$ such that $BE \perp AC$, and suppose that $DE \cap AC = \{N\}$. Show that:
$$
AN = 2 \cdot AB.
$$
$$
AN = 2 \cdot AB.
$$