{"status": "success", "data": {"description_md": "In the right triangle $\\triangle ACE$, we have $AC=12$, $CE=16$, and $EA=20$. Points $B$, $D$, and $F$ are located on $AC$, $CE$, and $EA$, respectively, so that $AB=3$, $CD=4$, and $EF=5$. What is the ratio of the area of $\\triangle DBF$ to that of $\\triangle ACE$?\n\n
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\n\n$\\mathrm{(A) \\ } \\frac{1}{4} \\qquad \\mathrm{(B) \\ } \\frac{9}{25} \\qquad \\mathrm{(C) \\ } \\frac{3}{8} \\qquad \\mathrm{(D) \\ } \\frac{11}{25} \\qquad \\mathrm{(E) \\ } \\frac{7}{16}$", "description_html": "

In the right triangle \\triangle ACE , we have AC=12 , CE=16 , and EA=20 . Points B , D , and F are located on AC , CE , and EA , respectively, so that AB=3 , CD=4 , and EF=5 . What is the ratio of the area of \\triangle DBF to that of \\triangle ACE ?

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\\mathrm{(A) \\ } \\frac{1}{4} \\qquad \\mathrm{(B) \\ } \\frac{9}{25} \\qquad \\mathrm{(C) \\ } \\frac{3}{8} \\qquad \\mathrm{(D) \\ } \\frac{11}{25} \\qquad \\mathrm{(E) \\ } \\frac{7}{16}

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Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2004 AMC 10B Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc10B_p19", "prev": "/problem/04_amc10B_p17"}}