{"status": "success", "data": {"description_md": "**POTD Challenge December 17, 2023**\n**Author:** excelex\n\nA regular 11-gon $A_1 A_2 A_3... A_{11}$ has circumradius $1$ and circumcenter $O$. Point $P$ is constructed such that $\\angle OA_1P=90^{\\circ}$, $\\angle POA_1= 60^{\\circ}$, and $\\angle A_1PO=30^{\\circ}$ . In other words, $\\triangle OPA_1$ is a $30-60-90$ triangle with smallest side being $OA_1$. If $N$ is the value of $\\prod_{i=1}^{11} A_i P$, find the remainder when $N^2$ is divided by $1000$.", "description_html": "<p><strong>POTD Challenge December 17, 2023</strong><br/>&#10;<strong>Author:</strong> excelex</p>&#10;<p>A regular 11-gon <span class=\"katex--inline\">A_1 A_2 A_3... A_{11}</span> has circumradius <span class=\"katex--inline\">1</span> and circumcenter <span class=\"katex--inline\">O</span>. Point <span class=\"katex--inline\">P</span> is constructed such that <span class=\"katex--inline\">\\angle OA_1P=90^{\\circ}</span>, <span class=\"katex--inline\">\\angle POA_1= 60^{\\circ}</span>, and <span class=\"katex--inline\">\\angle A_1PO=30^{\\circ}</span> . In other words, <span class=\"katex--inline\">\\triangle OPA_1</span> is a <span class=\"katex--inline\">30-60-90</span> triangle with smallest side being <span class=\"katex--inline\">OA_1</span>. If <span class=\"katex--inline\">N</span> is the value of <span class=\"katex--inline\">\\prod_{i=1}^{11} A_i P</span>, find the remainder when <span class=\"katex--inline\">N^2</span> is divided by <span class=\"katex--inline\">1000</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "Problem of the Day #28 (Challenge)", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}