# A tight fit ....

Geometry Level 5

A circle of (non-zero) radius $$r$$ is positioned so that it is tangent to both $$y = \sqrt{x}$$ and the positive $$x$$-axis. Another circle, again of the same radius $$r$$, is positioned so that it is tangent to both $$y = \sqrt{x}$$ and the positive $$y$$-axis.

There is a unique value of $$r$$ so that the two circles described above, both of radius $$r$$, are also tangent to one another. Find $$\lfloor 10000*r \rfloor$$.

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