2024 AIME I Problems/Problem 8
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.
