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