There are two circles, one with center \(A\) and radius 1, the other with center \(B\) and radius 2. The distance \(AB\) is 6. A third circle of unknown radius is tangent to both of these circles and there exists a straight line which

**(1)** is tangent to all three circles, and

**(2)** intersects the segment \(AB\).

Find the radius of the third circle.

There are two solutions, \(R\) and \(r\). Evaluate \( R - r \).

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