quoted from Contest Analysis

"We can subtract from the radius of each of the three plants the
radius of the smallest plant, then compute an inversion about that
plant's center. Then we find appropriate tangents to the two inverted
plants, re-invert to find the corresponding circle, and add back the
radius of the smallest plant. "

I got puzzled when trying to understand this(may caused by my poor
English).
Why doing all these inversions? Doe "appropriate tangents" mean a
tangents go through the smallest plant's center?
And finally,how does this solution work?

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