Question 98
Let $ABC$ be a triangle. Let $X$ be the point on side $\overline{AB}$ such that $\angle BXC = 60^{\circ}$. Let $P$ be the point on segment $\overline{CX}$ such that $BP \perp AC$. Given that $AB = 6$, $AC = 7$, and $BP = 4$, compute $CP$.