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 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, D are collinear, XC = 67, XY = 47, and XD = 37. Find AB^2.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.