2022 AMC 10B 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?

\textbf{(A)}~48\pi\qquad\textbf{(B)}~68\pi\qquad\textbf{(C)}~96\pi\qquad\textbf{(D)}~102\pi\qquad\textbf{(E)}~136\pi\qquad

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.