# 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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