Question 177
A square $ABCD$ has a side length equal to $3$. Let $P$ be the point on the side $AB$ dividing $AB$ into $2 : 1$ ratio. Let $Q$, $R$ be the points on the side $CD$ dividing $CD$ into $1 : 2$, $2 : 1$ ratio, respectively. And let $S$, $T$ be the points on the side $DA$ dividing $DA$ into $1 : 2$, $2 : 1$ ratio, respectively. Let $U$ be the point of intersection of the lines $PR$ and $QT$, and $V$ be the point of intersection of the lines $SU$ and $BC$. Find the length of the line segment $BV$.
