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AIME 2024 / AIME 2024 train ec28d7b6-51c8-5477-a0a2-89eba61dc380
Problem
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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 .
Plain-text mathematical notation (without MathML)
Eight circles of radius 34 are sequentially tangent, and two of the circles are tangent to AB and BC of triangle ABC, respectively. 2024 circles of radius 1 can be arranged in the same manner. The inradius of triangle ABC can be expressed as (m)/(n), where m and n are relatively prime positive integers. Find m+n.
Original LaTeX notation
Eight circles of radius $34$ are sequentially tangent, and two of the circles are tangent to $AB$ and $BC$ of triangle $ABC$, respectively. $2024$ circles of radius $1$ can be arranged in the same manner. The inradius of triangle $ABC$ can be expressed as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.Discussion
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