# 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 $AB^2$.