2022 AMC 10A Problem 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 \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?

\textbf{(A) } 260 \qquad \textbf{(B) } 855 \qquad \textbf{(C) } 1235 \qquad \textbf{(D) } 1565 \qquad \textbf{(E) } 1997

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.