Four circles with radii 1, 2, 3, and $r$ are externally tangent to one another, where $r$ is the smallest radius.  Compute $r$.
Question:
Four circles with radii 1, 2, 3, and $r$ are externally tangent to one another, where $r$ is the smallest radius.  Compute $r$.
Answer:
Let's think step by step.

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\frac{6}{23}
Four circles with radii 1, 2, 3, and $r$ are externally tangent to one another, where $r$ is the smallest radius.  Compute $r$.
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