Question 75
Consider an equilateral triangle $ABC$ with each side measuring $10$. A circle passing through $A$ touches the side $BC$ (excluding the endpoints) at point $X$, and intersects sides $AB$ and $AC$ at points $D$ and $E$ respectively, both of which are different from point $A$. Given that $BX \gt CX$ and $AD + AE = 13$, find the length of segment $BX$.
