The radii of two circles are 9 cm and 12 cm. The circumference of a circle whose area is equal to sum of the areas of the two circles is:

Using the circle area formula, pi times radius squared, the sum of the areas of the two circles is pi times 9 squared plus pi times 12 squared, which equals 81 pi plus 144 pi, totaling 225 pi. Setting this equal to the larger circle's area gives pi times the large radius squared equals 225 pi, meaning the large radius squared is 225 and the radius is 15. The circumference formula, 2 times pi times radius, gives 2 times pi times 15, resulting in 30 pi centimeters.

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