{"status": "success", "data": {"description_md": "Convex quadrilateral $ABCD$ has $AB = 9$ and $CD = 12$.  Diagonals $AC$ and $BD$ intersect at $E$, $AC = 14$, and $\\triangle AED$ and $\\triangle BEC$ have equal areas.  What is $AE$?\n\n$\\textbf{(A)}\\ \\frac {9}{2}\\qquad \\textbf{(B)}\\ \\frac {50}{11}\\qquad \\textbf{(C)}\\ \\frac {21}{4}\\qquad \\textbf{(D)}\\ \\frac {17}{3}\\qquad \\textbf{(E)}\\ 6$\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>Convex quadrilateral  <span class=\"katex--inline\">ABCD</span>  has  <span class=\"katex--inline\">AB = 9</span>  and  <span class=\"katex--inline\">CD = 12</span> .  Diagonals  <span class=\"katex--inline\">AC</span>  and  <span class=\"katex--inline\">BD</span>  intersect at  <span class=\"katex--inline\">E</span> ,  <span class=\"katex--inline\">AC = 14</span> , and  <span class=\"katex--inline\">\\triangle AED</span>  and  <span class=\"katex--inline\">\\triangle BEC</span>  have equal areas.  What is  <span class=\"katex--inline\">AE</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac {9}{2}\\qquad \\textbf{(B)}\\ \\frac {50}{11}\\qquad \\textbf{(C)}\\ \\frac {21}{4}\\qquad \\textbf{(D)}\\ \\frac {17}{3}\\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": "2009 AMC 12A Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc12A_p21", "prev": "/problem/09_amc12A_p19"}}