{"status": "success", "data": {"description_md": "In the Cartesian plane let $A = (1,0)$ and $B = \\left( 2, 2\\sqrt{3} \\right)$. Equilateral triangle $ABC$ is constructed so that $C$ lies in the first quadrant. Let $P=(x,y)$ be the center of $\\triangle ABC$. Then $x \\cdot y$ can be written as $\\tfrac{p\\sqrt{q}}{r}$, where $p$ and $r$ are relatively prime positive integers and $q$ is an integer that 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": "

In the Cartesian plane let A = (1,0) and B = \\left( 2, 2\\sqrt{3} \\right). Equilateral triangle ABC is constructed so that C lies in the first quadrant. Let P=(x,y) be the center of \\triangle ABC. Then x \\cdot y can be written as \\tfrac{p\\sqrt{q}}{r}, where p and r are relatively prime positive integers and q is an integer that is not divisible by the square of any prime. Find p+q+r.

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": 3, "problem_name": "2013 AIME II Problem 4", "can_next": true, "can_prev": true, "nxt": "/problem/13_aime_II_p05", "prev": "/problem/13_aime_II_p03"}}