Mickey's Super-earsGeometry 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.