The Ins And Outs Of Circles

Geometry Level 3

\[\begin{cases} \begin{align} x^2 + y^2 &\leq 1 \\ (x-1)^2 + (y-1)^2 &\geq 1 \\ (x+1)^2 + (y+1)^2 &\geq 1 \\ \end{align} \end{cases}\]

Let \(D\) be the domain of the system of inequalities shown above. What is the area of \(D\)?

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