{"status": "success", "data": {"description_md": "In a plane, four circles with radii $1,3,5,$ and $7$ are tangent to line $\\ell$ at the same point $A,$ but they may be on either side of $\\ell$. Region $S$ consists of all the points that lie inside exactly one of the four circles. What is the maximum possible area of region $S$?\n\n$\\textbf{(A) }24\\pi \\qquad \\textbf{(B) }32\\pi \\qquad \\textbf{(C) }64\\pi \\qquad \\textbf{(D) }65\\pi \\qquad \\textbf{(E) }84\\pi$", "description_html": "<p>In a plane, four circles with radii  <span class=\"katex--inline\">1,3,5,</span>  and  <span class=\"katex--inline\">7</span>  are tangent to line  <span class=\"katex--inline\">\\ell</span>  at the same point  <span class=\"katex--inline\">A,</span>  but they may be on either side of  <span class=\"katex--inline\">\\ell</span> . Region  <span class=\"katex--inline\">S</span>  consists of all the points that lie inside exactly one of the four circles. What is the maximum possible area of region  <span class=\"katex--inline\">S</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) }24\\pi \\qquad \\textbf{(B) }32\\pi \\qquad \\textbf{(C) }64\\pi \\qquad \\textbf{(D) }65\\pi \\qquad \\textbf{(E) }84\\pi</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": 1, "problem_name": "2021 AMC 10B Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc10B_p08", "prev": "/problem/21_amc10B_p06"}}