Question 19
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 $\dfrac{PQ}{EF}?$
