# Touchy Circles

Geometry Level 3

Circles $$A$$ and $$B$$ are placed in the first quadrant so that circle $$A$$ is tangent to both the $$x$$-axis and the $$y$$-axis while circle $$B$$ is tangent to the $$x$$-axis and is externally tangent to circle $$A$$.

If the radius of circle $$B$$ is half the radius of circle $$A$$, then what is the slope of the line passing through the centers of $$A$$ and $$B$$?

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