Question 10
Let $\triangle ABC$ be an equilateral triangle with side length $6$. Let $P$ be a point inside triangle $\triangle ABC$ such that $\angle BPC = 120^\circ$. The circle with diameter $\overline{AP}$ meets the circumcircle of $\triangle ABC$ again at $X \neq A$. Given that $AX = 5$, compute $XP$.