{"status": "success", "data": {"description_md": "Let $A$ and $B$ be the endpoints of a semicircular arc of radius $2$. The arc is divided into seven congruent arcs by six equally spaced points $C_1,C_2,\\ldots,C_6$. All chords of the form $\\overline{AC_i}$ or $\\overline{BC_i}$ are drawn. Let $n$ be the product of the lengths of these twelve chords. Find the remainder when $n$ is divided by $1000$.\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> and <span class=\"katex--inline\">B</span> be the endpoints of a semicircular arc of radius <span class=\"katex--inline\">2</span>. The arc is divided into seven congruent arcs by six equally spaced points <span class=\"katex--inline\">C_1,C_2,\\ldots,C_6</span>. All chords of the form <span class=\"katex--inline\">\\overline{AC_i}</span> or <span class=\"katex--inline\">\\overline{BC_i}</span> are drawn. Let <span class=\"katex--inline\">n</span> be the product of the lengths of these twelve chords. Find the remainder when <span class=\"katex--inline\">n</span> is divided by <span class=\"katex--inline\">1000</span>.</p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "2009 AIME II Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/09_aime_II_p14", "prev": "/problem/09_aime_II_p12"}}