No way out

Calculus Level 5

Let \(S\) be the region in the first quadrant which is

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

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

Let \(r\) be the radius of the largest circle which can be inscribed in \(S\). Find \(\lfloor 10000*r \rfloor\).


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