Question 15
Quadrilateral $ABCD$ with side lengths $AB = 7,$ $BC = 24,$ $CD = 20,$ $DA = 15$ is inscribed in a circle. The area interior to the circle but exterior to the quadrilateral can be written in the form $\dfrac{a \pi - b}{c},$ where $a,$ $b,$ and $c$ are positive integers such that $a$ and $c$ have no common prime factor. What is $a + b + c?$