Question 166
A triangle $X Y Z$ and a circle $\omega$ of radius $2$ are given in a plane, such that $\omega$ intersects segment $\overline{X Y}$ at the points $A, B$, segment $\overline{Y Z}$ at the points $C, D$, and segment $\overline{Z X}$ at the points $E, F$. Suppose that $X B \gt X A$, $Y D \gt Y C$, and $Z F \gt Z E$. In addition, $X A = 1$, $Y C = 2$, $Z E = 3$, and $A B = C D = E F$. Compute $A B$.