{"status": "success", "data": {"description_md": "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 $a+b+c?$\n\n$\\textbf{(A) } 260 \\qquad \\textbf{(B) } 855 \\qquad \\textbf{(C) } 1235 \\qquad \\textbf{(D) } 1565 \\qquad \\textbf{(E) } 1997$", "description_html": "<p>Quadrilateral  <span class=\"katex--inline\">ABCD</span>  with side lengths  <span class=\"katex--inline\">AB=7, BC=24, CD=20, DA=15</span>  is inscribed in a circle. The area interior to the circle but exterior to the quadrilateral can be written in the form  <span class=\"katex--inline\">\\frac{a\\pi-b}{c},</span>  where  <span class=\"katex--inline\">a,b,</span>  and  <span class=\"katex--inline\">c</span>  are positive integers such that  <span class=\"katex--inline\">a</span>  and  <span class=\"katex--inline\">c</span>  have no common prime factor. What is  <span class=\"katex--inline\">a+b+c?</span> </p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 260 \\qquad \\textbf{(B) } 855 \\qquad \\textbf{(C) } 1235 \\qquad \\textbf{(D) } 1565 \\qquad \\textbf{(E) } 1997</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2022 AMC 10A Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc10A_p16", "prev": "/problem/22_amc10A_p14"}}