{"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$\\mathrm{(A)}\\ \\frac{9}{2}\n\\qquad\n\\mathrm{(B)}\\ \\frac{50}{11}\n\\qquad\n\\mathrm{(C)}\\ \\frac{21}{4}\n\\qquad\n\\mathrm{(D)}\\ \\frac{17}{3}\n\\qquad\n\\mathrm{(E)}\\ 6$", "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>\n<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ \\frac{9}{2}\n\\qquad\n\\mathrm{(B)}\\ \\frac{50}{11}\n\\qquad\n\\mathrm{(C)}\\ \\frac{21}{4}\n\\qquad\n\\mathrm{(D)}\\ \\frac{17}{3}\n\\qquad\n\\mathrm{(E)}\\ 6</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": 4, "problem_name": "2009 AMC 10A Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc10A_p24", "prev": "/problem/09_amc10A_p22"}}