Geometry Level 3

Two congruent circles $$\Gamma_1$$ and $$\Gamma_2$$ each have radius $$213,$$ and the center of $$\Gamma_1$$ lies on $$\Gamma_2.$$ Suppose $$\Gamma_1$$ and $$\Gamma_2$$ intersect at $$A$$ and $$B$$. The line through $$A$$ perpendicular to $$AB$$ meets $$\Gamma_1$$ and $$\Gamma_2$$ again at $$C$$ and $$D$$, respectively. Find the length of $$CD$$.

This problem is posed by Muhammad A.

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