Question 88
Let $ABCD$ be a rectangle with $AB = 6$ and $BC = 4$. Let $E$ be the point on $BC$ with $BE = 3$, and let $F$ be the point on segment $AE$ such that $F$ lies halfway between the segments $AB$ and $CD$. If $G$ is the point of intersection of $DF$ and $BC$, find $BG$.