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2016 AMC 10B Problems/Problem 19

Revision as of 09:24, 21 February 2016 by Mathlogin (talk | contribs) (Created page with "==Problem== Rectangle <math>ABCD</math> has <math>AB=5</math> and <math>BC=4</math>. Point <math>E</math> lies on line <math>AB</math> so that <math>EB=1</math>, point <math>...")
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Problem

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

\[(A) \frac{\sqrt{3}}{16}, (B) \frac{\sqrt{2}}{13}, (C), \frac{9}{82}, (D) \frac{10}{91}, (E) \frac{1}{9}\]

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