Question 178
Points $A$, $B$, $C$, and $D$ lie on a line $\ell$ in that order, with $AB = CD = 4$ and $BC = 8$. Circles $\Omega_1$, $\Omega_2$, and $\Omega_3$ with diameters $AB$, $BC$, and $CD$, respectively, are drawn. A line through $A$ and tangent to $\Omega_3$ intersects $\Omega_2$ at the two points $X$ and $Y$. Find the length of $XY$.
