A tight fit ....

Geometry Level 5

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

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

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