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2016 AMC 10B Problem 19

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2016 AMC 10B Problem 19AMC 10 Step by Step

Name: Date: September 13, 2026

Similar & Congruent Triangles · difficulty 3 of 5 · about 6 min · position P16-20

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 $\frac{PQ}{EF}$ ?

A)
$\frac{\sqrt{13}}{16}$
B)
$\frac{\sqrt{2}}{13}$
C)
$\frac{9}{82}$
D)
$\frac{10}{91}$
E)
$\frac19$

2016 AMC 10B Problem 19

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