AMC 10 Step by Step
2022 AMC 10BProblem 22P21-25~7 minPrint

Let SS be the set of circles in the coordinate plane that are tangent to each of the three circles with equations x2+y2=4x^{2}+y^{2}=4 , x2+y2=64x^{2}+y^{2}=64 , and (x5)2+y2=3(x-5)^{2}+y^{2}=3 . What is the sum of the areas of all circles in SS ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.