# Snuggle Up

Geometry Level 3

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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