{"status": "success", "data": {"description_md": "Two circles lie outside regular hexagon $ABCDEF$. The first is tangent to $\\overline{AB}$, and the second is tangent to $\\overline{DE}$. Both are tangent to lines $BC$ and $FA$. What is the ratio of the area of the second circle to that of the first circle?\n\n$\\textbf{(A)}\\ 18\n\\qquad\n\\textbf{(B)}\\ 27\n\\qquad\n\\textbf{(C)}\\ 36\n\\qquad\n\\textbf{(D)}\\ 81\n\\qquad\n\\textbf{(E)}\\ 108$", "description_html": "<p>Two circles lie outside regular hexagon  <span class=\"katex--inline\">ABCDEF</span> . The first is tangent to  <span class=\"katex--inline\">\\overline{AB}</span> , and the second is tangent to  <span class=\"katex--inline\">\\overline{DE}</span> . Both are tangent to lines  <span class=\"katex--inline\">BC</span>  and  <span class=\"katex--inline\">FA</span> . What is the ratio of the area of the second circle to that of the first circle?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 18\n\\qquad\n\\textbf{(B)}\\ 27\n\\qquad\n\\textbf{(C)}\\ 36\n\\qquad\n\\textbf{(D)}\\ 81\n\\qquad\n\\textbf{(E)}\\ 108</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": "2010 AMC 10B Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc10B_p21", "prev": "/problem/10_amc10B_p19"}}