AMC 10B 2022 Problem 22

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
A. 48 \pi
B. 68 \pi
C. 96 \pi
D. 102 \pi
E. 136 \pi