{"status": "success", "data": {"description_md": "In $\\triangle ABC$ points $D$ and $E$ lie on $BC$ and $AC$, respectively. If $AD$ and $BE$ intersect at $T$ so that $\\frac{AT}{DT}=3$ and $\\frac{BT}{ET}=4$, what is $\\frac{CD}{BD}$?\n\n
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\n\n$\\mathrm{(A) \\ } \\frac{1}{8} \\qquad \\mathrm{(B) \\ } \\frac{2}{9} \\qquad \\mathrm{(C) \\ } \\frac{3}{10} \\qquad \\mathrm{(D) \\ } \\frac{4}{11} \\qquad \\mathrm{(E) \\ } \\frac{5}{12}$", "description_html": "

In \\triangle ABC points D and E lie on BC and AC , respectively. If AD and BE intersect at T so that \\frac{AT}{DT}=3 and \\frac{BT}{ET}=4 , what is \\frac{CD}{BD} ?

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\\mathrm{(A) \\ } \\frac{1}{8} \\qquad \\mathrm{(B) \\ } \\frac{2}{9} \\qquad \\mathrm{(C) \\ } \\frac{3}{10} \\qquad \\mathrm{(D) \\ } \\frac{4}{11} \\qquad \\mathrm{(E) \\ } \\frac{5}{12}

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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 20", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc10B_p21", "prev": "/problem/04_amc10B_p19"}}