CN-LEAGUE 2000 Problem 1

In acute-angled triangle $ABC,$ $E,F$ are on the side $BC,$ such that $\angle BAE=\angle CAF,$ and let $M,N$ be the projections of $F$ onto $AB,AC,$ respectively. The line $AE$ intersects $\odot (ABC)$ at $D$ (different from point $A$ ). Prove that $S_{AMDN}=S_{\triangle ABC}.$