{"status": "success", "data": {"description_md": "In $ABC$ we have $AB = 25$, $BC = 39$, and $AC=42$. Points $D$ and $E$ are on $AB$ and $AC$ respectively, with $AD = 19$ and $AE = 14$. What is the ratio of the area of triangle $ADE$ to the area of the quadrilateral $BCED$?\n\n$\\mathrm{(A) \\ } \\frac{266}{1521}\\qquad \\mathrm{(B) \\ } \\frac{19}{75}\\qquad \\mathrm{(C) \\ } \\frac{1}{3}\\qquad \\mathrm{(D) \\ } \\frac{19}{56}\\qquad \\mathrm{(E) \\ } 1$", "description_html": "<p>In  <span class=\"katex--inline\">ABC</span>  we have  <span class=\"katex--inline\">AB = 25</span> ,  <span class=\"katex--inline\">BC = 39</span> , and  <span class=\"katex--inline\">AC=42</span> . Points  <span class=\"katex--inline\">D</span>  and  <span class=\"katex--inline\">E</span>  are on  <span class=\"katex--inline\">AB</span>  and  <span class=\"katex--inline\">AC</span>  respectively, with  <span class=\"katex--inline\">AD = 19</span>  and  <span class=\"katex--inline\">AE = 14</span> . What is the ratio of the area of triangle  <span class=\"katex--inline\">ADE</span>  to the area of the quadrilateral  <span class=\"katex--inline\">BCED</span> ?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } \\frac{266}{1521}\\qquad \\mathrm{(B) \\ } \\frac{19}{75}\\qquad \\mathrm{(C) \\ } \\frac{1}{3}\\qquad \\mathrm{(D) \\ } \\frac{19}{56}\\qquad \\mathrm{(E) \\ } 1</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": "2005 AMC 10A Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/05_amc10A_p24"}}