{"status": "success", "data": {"description_md": "Let $a$, $b$, $c$ be the three sides of a triangle, and let $\\alpha$, $\\beta$, $\\gamma$, be the angles opposite them. If $a^2+b^2=1989c^2$, find $$ \\frac{\\cot \\gamma}{\\cot \\alpha+\\cot \\beta}. $$\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>Let <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span>, <span class=\"katex--inline\">c</span> be the three sides of a triangle, and let <span class=\"katex--inline\">\\alpha</span>, <span class=\"katex--inline\">\\beta</span>, <span class=\"katex--inline\">\\gamma</span>, be the angles opposite them. If <span class=\"katex--inline\">a^2+b^2=1989c^2</span>, find <span class=\"katex--display\"> \\frac{\\cot \\gamma}{\\cot \\alpha+\\cot \\beta}. </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": 5, "problem_name": "1989 AIME Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/89_aime_p11", "prev": "/problem/89_aime_p09"}}