Geometry- The king of shapes

Geometry Level 5

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 \({AB}^2\).


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