Question 49
Let $\triangle ABC$ be a triangle with $AB = 7$, $BC = 1$, and $CA = 4\sqrt{3}$. The angle trisectors of $C$ intersect $\overline{AB}$ at $D$ and $E$, and lines $\overline{AC}$ and $\overline{BC}$ intersect the circumcircle of $\triangle CDE$ again at $X$ and $Y$, respectively. Find the length of $XY$.