Sum of areas tangent to three circles

1750AdeptCoordinate GeometryGeometry

AMC 12B · 2022 · Problem 21

Let $S$ be the set of circles in the coordinate plane that are tangent to each of the three circles with equations $x^{2}+y^{2}=4$, $x^{2}+y^{2}=64$, and $(x-5)^{2}+y^{2}=3$. What is the sum of the areas of all circles in $S$?

Answer choices

48 \pi

68 \pi

96 \pi

102 \pi

136 \pi

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