Quadrilateral $ABCD$ with side lengths $AB=14$, $BC=48$, $CD=40$, $DA=30$ is inscribed in a circle. The area interior to the circle but exterior to the quadrilateral can be written in the form $\frac{a\pi -b}{c}$, where $a,b,$ and $c$ are positive integers such that $a$ and $c$ have no common prime factor. What is $a+b+c$?