{"status": "success", "data": {"description_md": "In rectangle $ABCD$, $DC=2 \\cdot CB$ and points $E$ and $F$ lie on $\\overline{AB}$ so that $\\overline{ED}$ and $\\overline{FD}$ trisect $\\angle ADC$ as shown. What is the ratio of the area of $\\triangle DEF$ to the area of rectangle $ABCD$?\n\n
\n\n
\n\n$\\textbf{(A)}\\ \\ \\frac{\\sqrt{3}}{6}\\qquad\\textbf{(B)}\\ \\frac{\\sqrt{6}}{8}\\qquad\\textbf{(C)}\\ \\frac{3\\sqrt{3}}{16}\\qquad\\textbf{(D)}\\ \\frac{1}{3}\\qquad\\textbf{(E)}\\ \\frac{\\sqrt{2}}{4}$", "description_html": "

In rectangle ABCD , DC=2 \\cdot CB and points E and F lie on \\overline{AB} so that \\overline{ED} and \\overline{FD} trisect \\angle ADC as shown. What is the ratio of the area of \\triangle DEF to the area of rectangle ABCD ?

\n
\n\n
\n

\\textbf{(A)}\\ \\ \\frac{\\sqrt{3}}{6}\\qquad\\textbf{(B)}\\ \\frac{\\sqrt{6}}{8}\\qquad\\textbf{(C)}\\ \\frac{3\\sqrt{3}}{16}\\qquad\\textbf{(D)}\\ \\frac{1}{3}\\qquad\\textbf{(E)}\\ \\frac{\\sqrt{2}}{4}

\n

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": "2014 AMC 10B Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/14_amc10B_p16", "prev": "/problem/14_amc10B_p14"}}