Difference between revisions of "2024 AIME I Problems/Problem 8"
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| + | ==Problem== | ||
| + | Eight circles of radius <math>34</math> are sequentially tangent, and two of the circles are tangent to <math>AB</math> and <math>BC</math> of triangle <math>ABC</math>, respectively. <math>2024</math> circles of radius <math>1</math> can be arranged in the same manner. The inradius of triangle <math>ABC</math> can be expressed as <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>. | ||
| + | ==Solution== | ||
| + | Notice that the incircle is the same as a case with one circle of <math>x</math> radius. | ||
Revision as of 13:55, 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.
