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Geometry Level 5

Suppose we have a square \(ABCD\) with corners \(A(0,0), B(0,2), C(2,2), D(2,0)\).

If a circle with center \(O(-1,-1)\) and radius \(r\) is such that half of the square's area lies within the circle, what is \(\lfloor 1000*r \rfloor\)?

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