{"status": "success", "data": {"description_md": "In equilateral $\\triangle ABC$ let points $D$ and $E$ trisect $\\overline{BC}$. Then $\\sin \\left( \\angle DAE \\right)$ can be expressed in the form $\\tfrac{a\\sqrt{b}}{c}$, where $a$ and $c$ are relatively prime positive integers, and $b$ is an integer that is not divisible by the square of any prime. Find $a+b+c$.\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 equilateral <span class=\"katex--inline\">\\triangle ABC</span> let points <span class=\"katex--inline\">D</span> and <span class=\"katex--inline\">E</span> trisect <span class=\"katex--inline\">\\overline{BC}</span>. Then <span class=\"katex--inline\">\\sin \\left( \\angle DAE \\right)</span> can be expressed in the form <span class=\"katex--inline\">\\tfrac{a\\sqrt{b}}{c}</span>, where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">c</span> are relatively prime positive integers, and <span class=\"katex--inline\">b</span> is an integer that is not divisible by the square of any prime. Find <span class=\"katex--inline\">a+b+c</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": "2013 AIME II Problem 5", "can_next": true, "can_prev": true, "nxt": "/problem/13_aime_II_p06", "prev": "/problem/13_aime_II_p04"}}