Difference between revisions of "2024 AIME I Problems/Problem 8"
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==Solution== | ==Solution== | ||
Notice that the incircle is the same as a case with one circle of <math>x</math> radius. | Notice that the incircle is the same as a case with one circle of <math>x</math> radius. | ||
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| + | ==See also== | ||
| + | {{AIME box|year=2024|n=I|num-b=7|num-a=9}} | ||
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| + | {{MAA Notice}} | ||
Revision as of 13:59, 2 February 2024
Problem
Eight circles of radius 
are sequentially tangent, and two of the circles are tangent to 
and 
of triangle 
, respectively. 
circles of radius 
can be arranged in the same manner. The inradius of triangle can be expressed as 
, where 
and 
are relatively prime positive integers. Find 
.
Solution
Notice that the incircle is the same as a case with one circle of 
radius.
See also
| 2024 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
