{"status": "success", "data": {"description_md": "In a circle, parallel chords of lengths 2, 3, and 4 determine central angles of $\\alpha$, $\\beta$, and $\\alpha + \\beta$ radians, respectively, where $\\alpha + \\beta < \\pi$. If $\\cos \\alpha$, which is a positive rational number, is expressed as a fraction in lowest terms, what is the sum of its numerator and denominator?\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 a circle, parallel chords of lengths 2, 3, and 4 determine central angles of <span class=\"katex--inline\">\\alpha</span>, <span class=\"katex--inline\">\\beta</span>, and <span class=\"katex--inline\">\\alpha + \\beta</span> radians, respectively, where <span class=\"katex--inline\">\\alpha + \\beta &lt; \\pi</span>. If <span class=\"katex--inline\">\\cos \\alpha</span>, which is a positive rational number, is expressed as a fraction in lowest terms, what is the sum of its numerator and denominator?</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": 4, "problem_name": "1985 AIME Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/85_aime_p10", "prev": "/problem/85_aime_p08"}}