AMC 10 2022b 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 $S$? $\textbf{(A)}~48\pi \textbf{(B)}~68\pi \textbf{(C)}~96\pi \textbf{(D)}~102\pi \textbf{(E)}~136\pi$