Question 119
$ABCDE$ is a cyclic convex pentagon, and $AC = BD = CE$. $AC$ and $BD$ intersect at $X$, and $BD$ and $CE$ intersect at $Y$. If $AX = 6$, $XY = 4$, and $YE = 7$, then the area of pentagon $ABCDE$ can be written as $\frac{a \sqrt{b}}{c}$, where $a, b, c$ are integers, $c$ is positive, $b$ is square-free, and $\operatorname{gcd}(a, c) = 1$. Find $100a + 10b + c$.