2016 AIME I Problem 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 A B closer to point X than to Y. Circle \omega passes through A and B intersecting \omega_{1} again at D \neq A and intersecting \omega_{2} again at C \neq B. The three points C, Y, and D are collinear, X C=67, X Y=47, and X D=37. Find A B^{2}.