As shown in the figure, three circles which have the same radius \(...

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As shown in the figure, three circles which have the same radius \( r \) have centers at \( (0,0),(1,1) \), and \( (2,1) \). If they have
\( \mathrm{P} \) a common tangent line, as shown, then the value of \( 10 \sqrt{5} r \)

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