{"status": "success", "data": {"description_md": "Eight circles of radius $34$ can be placed tangent to side $\\overline{BC}$ of $\\triangle ABC$ such that the first circle is tangent to $\\overline{AB}$, subsequent circles are externally tangent to each other, and the last is tangent to $\\overline{AC}$. Similarly, $2024$ circles of radius $1$ can also be placed along $\\overline{BC}$ in this manner. The inradius of $\\triangle ABC$ is $\\tfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

Eight circles of radius 34 can be placed tangent to side \\overline{BC} of \\triangle ABC such that the first circle is tangent to \\overline{AB}, subsequent circles are externally tangent to each other, and the last is tangent to \\overline{AC}. Similarly, 2024 circles of radius 1 can also be placed along \\overline{BC} in this manner. The inradius of \\triangle ABC is \\tfrac{m}{n}, where m and n are relatively prime positive integers. Find m+n.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2024 AIME I Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/24_aime_I_p09", "prev": "/problem/24_aime_I_p07"}}