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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_21 / Let S be the set of circles in the coordinate plane that are tangent to each of the three circles with equations x²+y²=4, x²+y²=64, and (x−5)²+y²=3. What is the sum of the areas of…

Problem

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problem

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

?Output the remainder when the answer is divided by 100.

Plain-text mathematical notation (without MathML)

Let S be the set of circles in the coordinate plane that are tangent to each of the three circles with equations x²+y²=4, x²+y²=64, and (x−5)²+y²=3. What is the sum of the areas of all circles in S?Output the remainder when the answer is divided by 100.

Original LaTeX notation

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 $S$?Output the remainder when the answer is divided by 100.

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_21
task_id: 587e62a8-8525-58e7-b9cd-13f811177364
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f21
task_revision_id: 2
config / split: default / train

Official source

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