2022 AMC 12B Problems/Problem 21
Problem
Let be the set of circles in the coordinate plane that are tangent to each of the three circles with equations , , and . What is the sum of the areas of all circles in ?
Solution
The circles match up as follows: Case 1 is brown, Case 2 is blue, Case 3 is green, and Case 4 is red.[/center]
Let
[*]
Consider Cases 1 and 4 together. Since circles
Consider Cases 2 and 3 together. Similarly to Case 1 and 4, the line connecting the center of
The set of circles S consists of 8 circles - 4 of which have radius 5 and 4 of which have radius 3.
The total area of all circles in S is
-naman12
2022 AMC 12B (Problems • Answer Key • Resources) | |
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Followed by Problem 22 |
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2022 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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