Question 46
Let $ABC$ be an acute triangle with circumcenter $O$ such that $AB = 4$, $AC = 5$, and $BC = 6$. Let $D$ be the foot of the altitude from $A$ to $BC$, and $E$ be the intersection of $AO$ with $BC$. Suppose that $X$ is on $BC$ between $D$ and $E$ such that there is a point $Y$ on $AD$ satisfying $XY \parallel AO$ and $YO \perp AX$. Determine the length of $BX$.
