MathDB
Tangent Circles in the Coordinate Plane

Source: 2022 AMC 10B #22 / 2022 AMC 12B #21

November 17, 2022
AMCAMC 10geometryAMC 122022 AMC2022 AMC 10B2022 AMC 12B

Problem Statement

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?
<spanclass=latexbold>(A)</span> 48π<spanclass=latexbold>(B)</span> 68π<spanclass=latexbold>(C)</span> 96π<spanclass=latexbold>(D)</span> 102π<spanclass=latexbold>(E)</span> 136π<span class='latex-bold'>(A)</span>~48\pi\qquad<span class='latex-bold'>(B)</span>~68\pi\qquad<span class='latex-bold'>(C)</span>~96\pi\qquad<span class='latex-bold'>(D)</span>~102\pi\qquad<span class='latex-bold'>(E)</span>~136\pi\qquad