No way out

Calculus Level 5

Let SS be the region in the first quadrant which is

(i) to the right of the parabola y=x2y = x^{2} and

(ii) to the left of the parabola y=(x2)2y = (x - 2)^{2}.

Let rr be the radius of the largest circle which can be inscribed in SS. Find 10000r\lfloor 10000*r \rfloor.

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