Math Gold Medalist

Lor

2022 AMC 12B 

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 $S$?

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

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   Solution