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Three circles of unit radius and centered at $\left ( 0,1.5 \right )$, $\left ( 0,-1.5 \right )$, and $\left ( 2,0 \right )$ are shown in dark blue color in the attached figure. The set of all circles that are tangent to all three of the given circles are drawn. What is the radius of the second largest such circle?
This started as a way to express the admins' love of calculus and math in general. As result, this has turned into a gathering place for math-based humor and weekly challenges.
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