Geometry- The king of shapes

Two circles intersect ${\omega}_{1}$ and ${\omega}_{2}$ each other at $X, Y$ .

Straight line through $A, B$ is a common tangent to both the circles ${\omega}_{1}$ and ${\omega}_{2}$ .

A line through Y intersects ${\omega}_{1}$ and ${\omega}_{2}$ at $C, D$ , respectively.

A circle ${\omega}$ passes through $A, B, C, D$ .

$XY = 47, XD = 37, XC = 67$ . $XC, XD$ do not pass through centers.

Ignore the centre of circles.

Find value of ${AB}^2$ .