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2022 AMC 10B Problem 22

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2022 AMC 10B Problem 22AMC 10 Step by Step
Name:                             Date: September 13, 2026
Circles · difficulty 4 of 5 · about 7 min · position P21-25

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 (x−5)2+y2=3(x-5)^{2}+y^{2}=3 . What is the sum of the areas of all circles in SS ?

  1. A)

    48π48\pi

  2. B)

    68π68\pi

  3. C)

    96π96\pi

  4. D)

    102π102\pi

  5. E)

    136π136\pi

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