Mickey's Super-ears

Geometry Level 5

Two lines intersect each other forming a right angle. A unit circle (radius 1) is tangent to both of these lines. Two equal size circles with radius \(R>1\) are:
(1) tangent to this circle,
(2) tangent to each other, and
(3) each tangent to one of the lines,

as shown in the figure above.

Calculate \(R\) to two decimal places.

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