{"status": "success", "data": {"description_md": "Andrea inscribed a circle inside a regular pentagon, circumscribed a circle around the pentagon, and calculated the area of the region between the two circles.  Bethany did the same with a regular heptagon (7 sides).  The areas of the two regions were $A$ and $B$, respectively.  Each polygon had a side length of $2$.  Which of the following is true?\n\n$\\textbf{(A)}\\ A = \\frac {25}{49}B\\qquad \\textbf{(B)}\\ A = \\frac {5}{7}B\\qquad \\textbf{(C)}\\ A = B\\qquad \\textbf{(D)}\\ A$ $= \\frac {7}{5}B\\qquad \\textbf{(E)}\\ A = \\frac {49}{25}B$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Andrea inscribed a circle inside a regular pentagon, circumscribed a circle around the pentagon, and calculated the area of the region between the two circles.  Bethany did the same with a regular heptagon (7 sides).  The areas of the two regions were  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">B</span> , respectively.  Each polygon had a side length of  <span class=\"katex--inline\">2</span> .  Which of the following is true?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ A = \\frac {25}{49}B\\qquad \\textbf{(B)}\\ A = \\frac {5}{7}B\\qquad \\textbf{(C)}\\ A = B\\qquad \\textbf{(D)}\\ A</span>   <span class=\"katex--inline\">= \\frac {7}{5}B\\qquad \\textbf{(E)}\\ A = \\frac {49}{25}B</span> </p>&#10;<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": "2009 AMC 12A Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc12A_p20", "prev": "/problem/09_amc12A_p18"}}