Question 21
In convex quadrilateral $A B C D$ we have $A B=15$, $B C=16$, $C D=12$, $D A=25$, and $B D=20$. Let $M$ and $\gamma$ denote the circumcenter and circumcircle of $\triangle A B D$. Line $C B$ meets $\gamma$ again at $F$, line $A F$ meets $M C$ at $G$, and line $G D$ meets $\gamma$ again at $E$. Determine the area of pentagon $A B C D E$.