{"status": "success", "data": {"description_md": "Rectangle $ABCD$ has $AB=5$ and $BC=4$. Point $E$ lies on $\\overline{AB}$ so that $EB=1$, point $G$ lies on $\\overline{BC}$ so that $CG=1$. and point $F$ lies on $\\overline{CD}$ so that $DF=2$. Segments $\\overline{AG}$ and $\\overline{AC}$ intersect $\\overline{EF}$ at $Q$ and $P$, respectively. What is the value of $\\frac{PQ}{EF}$?\n\n
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\n\n$\\textbf{(A)}~\\frac{\\sqrt{13}}{16} \\qquad\n\\textbf{(B)}~\\frac{\\sqrt{2}}{13} \\qquad\n\\textbf{(C)}~\\frac{9}{82} \\qquad\n\\textbf{(D)}~\\frac{10}{91}\\qquad\n\\textbf{(E)}~\\frac19$", "description_html": "

Rectangle ABCD has AB=5 and BC=4 . Point E lies on \\overline{AB} so that EB=1 , point G lies on \\overline{BC} so that CG=1 . and point F lies on \\overline{CD} so that DF=2 . Segments \\overline{AG} and \\overline{AC} intersect \\overline{EF} at Q and P , respectively. What is the value of \\frac{PQ}{EF} ?

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\\textbf{(A)}~\\frac{\\sqrt{13}}{16} \\qquad\n\\textbf{(B)}~\\frac{\\sqrt{2}}{13} \\qquad\n\\textbf{(C)}~\\frac{9}{82} \\qquad\n\\textbf{(D)}~\\frac{10}{91}\\qquad\n\\textbf{(E)}~\\frac19

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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": "2016 AMC 10B Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc10B_p20", "prev": "/problem/16_amc10B_p18"}}