Question 125
Let $ABC$ be an acute triangle and $D$ be the foot of altitude from $A$ to $\overline{BC}$. Let $X$ and $Y$ be points on the segment $\overline{BC}$ such that $\angle BAX = \angle YAC$, $BX = 2$, $XY = 6$, and $YC = 3$. Given that $AD = 12$, compute $BD$.