2023 AMC 12A Problems/Problem 18
Problem
Circle and each have radius , and the distance between their centers is . Circle is the largest circle internally tangent to both and . Circle is internally tangent to both and and externally tangent to . What is the radius of ?
[someone pls insert diagram]
Solution 1
With some simple geometry skills, we can find that has a radius of .
Since is internally tangent to , center of , and their tangent point must be on the same line.
Now, if we connect centers of , and /, we get a right angled triangle.
In which we get an equation by pythagorean theorem:
Solving it gives us
~lptoggled
See Also
2023 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 17 |
Followed by Problem 19 |
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