# Touchy Circles Part 2

Geometry Level 3

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

If a line passes through the centers of all three circles and the radii of circles $$B$$ and $$C$$ are equal, then how many times larger is the radius of circle $$A$$ than the radius of circle $$B$$?

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