Question 15
Circles $\omega_1$ and $\omega_2$ intersect at points $X$ and $Y.$ Line $\ell$ is tangent to $\omega_1$ and $\omega_2$ at $A$ and $B,$ respectively, with line $AB$ closer to point $X$ than to $Y.$ Circle $\omega$ passes through $A$ and $B$ intersecting $\omega_1$ again at $D \ne A$ and intersecting $\omega_2$ again at $C \ne B.$ The three points $C,$ $Y,$ $D$ are collinear, $XC = 67,$ $XY = 47,$ and $XD = 37.$ Find $AB^2.$