{"status": "success", "data": {"description_md": "Equiangular hexagon $ABCDEF$ has side lengths $AB=CD=EF=1$ and $BC=DE=FA=r$. The area of $\\triangle ACE$ is $70\\%$ of the area of the hexagon. What is the sum of all possible values of $r$?\n\n$\\textbf{(A)}\\ \\frac{4\\sqrt{3}}{3} \\qquad \\textbf{(B)} \\frac{10}{3} \\qquad \\textbf{(C)}\\ 4 \\qquad \\textbf{(D)}\\ \\frac{17}{4} \\qquad \\textbf{(E)}\\ 6$\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>Equiangular hexagon  <span class=\"katex--inline\">ABCDEF</span>  has side lengths  <span class=\"katex--inline\">AB=CD=EF=1</span>  and  <span class=\"katex--inline\">BC=DE=FA=r</span> . The area of  <span class=\"katex--inline\">\\triangle ACE</span>  is  <span class=\"katex--inline\">70\\%</span>  of the area of the hexagon. What is the sum of all possible values of  <span class=\"katex--inline\">r</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{4\\sqrt{3}}{3} \\qquad \\textbf{(B)} \\frac{10}{3} \\qquad \\textbf{(C)}\\ 4 \\qquad \\textbf{(D)}\\ \\frac{17}{4} \\qquad \\textbf{(E)}\\ 6</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": "2010 AMC 12A Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc12A_p18", "prev": "/problem/10_amc12A_p16"}}