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2022 AMC 10 A Problem 15

Source: 2022 AMC 10A #15

November 11, 2022
AMC 10AMCgeometrycyclic quadrilateral2022 AMC 10a2022 AMC

Problem Statement

Quadrilateral ABCDABCD with side lengths AB=7,BC=24,CD=20,DA=15AB=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 aπbc\frac{a\pi - b}{c}, where a,b,a, b, and cc are positive integers such that aa and cc have no common prime factor. What is a+b+ca+b+c?
<spanclass=latexbold>(A)</span>260<spanclass=latexbold>(B)</span>855<spanclass=latexbold>(C)</span>1235<spanclass=latexbold>(D)</span>1565<spanclass=latexbold>(E)</span>1997<span class='latex-bold'>(A) </span> 260 \qquad <span class='latex-bold'>(B) </span> 855 \qquad <span class='latex-bold'>(C) </span> 1235 \qquad <span class='latex-bold'>(D) </span> 1565 \qquad <span class='latex-bold'>(E) </span> 1997