托勒密证明题一

As shown in the figure, let $E$ and $F$be two points on the side $BC$ of an acute-angled triangle $\mathrm{\Delta }ABC$ such that $\mathrm{\angle }BAE=\mathrm{\angle }CAF$. Let $M$ and $N$be the projections of point $F$ onto $AB$ and $AC$, respectively. Extend $AE$ to intersect the circumcircle of $\mathrm{\Delta }ABC$ at point $D$. Prove that the area of quadrilateral $ADMN$ is equal to the area of $\mathrm{\Delta }ABC$.