{"status": "success", "data": {"description_md": "Pyramid $OABCD$ has square base $ABCD,$ congruent edges $\\overline{OA}, \\overline{OB}, \\overline{OC},$ and $\\overline{OD},$ and $\\angle AOB=45^\\circ.$ Let $\\theta$ be the measure of the dihedral angle formed by faces $OAB$ and $OBC.$ Given that $\\cos \\theta=m+\\sqrt{n},$ where $m$ and $n$ are integers, find $m+n.$\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>Pyramid <span class=\"katex--inline\">OABCD</span> has square base <span class=\"katex--inline\">ABCD,</span> congruent edges <span class=\"katex--inline\">\\overline{OA}, \\overline{OB}, \\overline{OC},</span> and <span class=\"katex--inline\">\\overline{OD},</span> and <span class=\"katex--inline\">\\angle AOB=45^\\circ.</span> Let <span class=\"katex--inline\">\\theta</span> be the measure of the dihedral angle formed by faces <span class=\"katex--inline\">OAB</span> and <span class=\"katex--inline\">OBC.</span> Given that <span class=\"katex--inline\">\\cos \\theta=m+\\sqrt{n},</span> where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are integers, find <span class=\"katex--inline\">m+n.</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": "1995 AIME Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/95_aime_p13", "prev": "/problem/95_aime_p11"}}