{"status": "success", "data": {"description_md": "In convex quadrilateral $ABCD$, $\\angle A \\cong \\angle C$, $AB = CD = 180$, and $AD \\neq BC$. The perimeter of $ABCD$ is 640. Find $\\lfloor 1000 \\cos A \\rfloor$. (The notation $\\lfloor x \\rfloor$ means the greatest integer that is less than or equal to $x$.)\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 convex quadrilateral <span class=\"katex--inline\">ABCD</span>, <span class=\"katex--inline\">\\angle A \\cong \\angle C</span>, <span class=\"katex--inline\">AB = CD = 180</span>, and <span class=\"katex--inline\">AD \\neq BC</span>. The perimeter of <span class=\"katex--inline\">ABCD</span> is 640. Find <span class=\"katex--inline\">\\lfloor 1000 \\cos A \\rfloor</span>. (The notation <span class=\"katex--inline\">\\lfloor x \\rfloor</span> means the greatest integer that is less than or equal to <span class=\"katex--inline\">x</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": "2003 AIME I Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/03_aime_I_p13", "prev": "/problem/03_aime_I_p11"}}