{"status": "success", "data": {"description_md": "A triangle has vertices $A(0,0)$, $B(12,0)$, and $C(8,10)$. The probability that a randomly chosen point inside the triangle is closer to vertex $B$ than to either vertex $A$ or vertex $C$ can be written as $\\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.\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>A triangle has vertices <span class=\"katex--inline\">A(0,0)</span>, <span class=\"katex--inline\">B(12,0)</span>, and <span class=\"katex--inline\">C(8,10)</span>. The probability that a randomly chosen point inside the triangle is closer to vertex <span class=\"katex--inline\">B</span> than to either vertex <span class=\"katex--inline\">A</span> or vertex <span class=\"katex--inline\">C</span> can be written as <span class=\"katex--inline\">\\frac{p}{q}</span>, where <span class=\"katex--inline\">p</span> and <span class=\"katex--inline\">q</span> are relatively prime positive integers. Find <span class=\"katex--inline\">p+q</span>.</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": 3, "problem_name": "2017 AIME II Problem 3", "can_next": true, "can_prev": true, "nxt": "/problem/17_aime_II_p04", "prev": "/problem/17_aime_II_p02"}}