# 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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