Six congruent circles are arranged so that each circle is externally tangent to at least two other circles. The centers of these six circles are then connected to form a polygon. If each circle has a radius of 2, then what is the perimeter of this polygon?

Since the centers of six externally tangent circles of radius 2 are connected to form a polygon, each side of this polygon equals the sum of their radii, which is 4. The perimeter of the six-sided polygon is 6 multiplied by 4. The perimeter is 24.

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