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This page uses JavaSketchpad. You may drag any of the red points, and the construction will adjust accordingly.

Explanation of the construction: Considering one of the given circles alone, the center of the desired circle must be at a distance of the sum of the two radii from the center of the the given circle. So the locus of the center of the new circle is a circle of radius the sum of the radii. The intersection of the two such circles gives the center of the common tangent circle. There is another common tangent circle centered at point J.

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