2016 AIME I #15

Circles \omega_1 and \omega_2 intersect at points X and Y. Line l 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 \neq A and intersecting \omega_2 again at C \neq B. The three points C, Y, and D are collinear, XC = 67, XY = 47, and XD = 37. Find AB^2.

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