lots of circles

Geometry Level pending

Two circles with radii r and 2r respectively touch each other externally. The radius of a circle that touches these two circles as well as a common tangents to the two circles, will be of the form (a/b +a sqrt(a))r. find a+b.

note:-the equation editor was not working properly.

Please add a nice solution. I cannot as I dont know ho to use LaTeX.

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