{"status": "success", "data": {"description_md": "The incircle of $\\omega$ of $\\triangle ABC$ is tangent to $\\overline{BC}$ at $X$. Let $Y \\neq X$ be the other intersection of $\\overline{AX}$ with $\\omega$. Points $P$ and $Q$ lie on $\\overline{AB}$ and $\\overline{AC}$, respectively, so that $\\overline{PQ}$ is tangent to $\\omega$ at $Y$. Assume that $AP=3, PB = 4, AC=8$, and $AQ = \\tfrac{m}{n}$, 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": "

The incircle of \\omega of \\triangle ABC is tangent to \\overline{BC} at X. Let Y \\neq X be the other intersection of \\overline{AX} with \\omega. Points P and Q lie on \\overline{AB} and \\overline{AC}, respectively, so that \\overline{PQ} is tangent to \\omega at Y. Assume that AP=3, PB = 4, AC=8, and AQ = \\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": 6, "problem_name": "2018 AIME II Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/18_aime_II_p15", "prev": "/problem/18_aime_II_p13"}}