HMMT 2025 G5

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 $XP$ .