Question 118
Let $ABC$ be an equilateral triangle. A regular hexagon $P X Q Y R Z$ of side length $2$ is placed so that $P$, $Q$, and $R$ lie on segments $\overline{BC}$, $\overline{CA}$, and $\overline{AB}$, respectively. If points $A$, $X$, and $Y$ are collinear, compute $BC$.