{"status": "success", "data": {"description_md": "In right triangle $ ABC$ with right angle at $ C$, $ \\angle BAC < 45$ degrees and $ AB = 4$. Point $ P$ on $ AB$ is chosen such that $ \\angle APC = 2\\angle ACP$ and $ CP = 1$. The ratio $ \\frac{AP}{BP}$ can be represented in the form $ p + q\\sqrt{r}$, where $ p,q,r$ are positive integers and $ r$ is not divisible by the square of any prime. Find $ p+q+r$.\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": "<p>In right triangle $ ABC$ with right angle at $ C$, $ \\angle BAC &lt; 45$ degrees and $ AB = 4$. Point $ P$ on $ AB$ is chosen such that $ \\angle APC = 2\\angle ACP$ and $ CP = 1$. The ratio $ \\frac{AP}{BP}$ can be represented in the form $ p + q\\sqrt{r}$, where $ p,q,r$ are positive integers and $ r$ is not divisible by the square of any prime. Find $ p+q+r$.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "2010 AIME II Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/10_aime_II_p15", "prev": "/problem/10_aime_II_p13"}}