Gently does it

Geometry Level 4

A circle of radius rr is positioned so that it has two points of tangency with the parabola y=x2y = x^{2}. Another circle, again of the same radius rr, is positioned (entirely in the first quadrant) so that it is tangent to both y=x2y = x^{2} and the positive xx-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. If r=abr = \dfrac{a}{b}, where aa and bb are positive coprime integers, then find a+ba + b.

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