The side $$𝐴𝐵$$ of a square $$𝐴𝐵𝐶𝐷$$ is $$1$$ and it is also a chord of a circle $$𝑆$$. The side $$𝐶𝐷$$ does not intersect $$𝑆$$. The length of the tangent $$𝐶𝐾$$, drawn from $$𝐶$$ to $$𝑆$$ at the point $$𝐾$$ is $$2$$. If $$𝑑$$ is the diameter of $$𝑆$$, then calculate $$d^{2}$$.

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