{"status": "success", "data": {"description_md": "**POTD March 20, 2024**\n\nLet $A_1A_2\\ldots A_{100}$ be a regular $100$-gon with a circumcircle of diameter $1$. Let $M$ be the midpoint of the minor arc $A_1A_2$. Find $\\sum\\limits_{i=1}^{100} |PA_i|^2$.", "description_html": "<p><strong>POTD March 20, 2024</strong></p>&#10;<p>Let <span class=\"katex--inline\">A_1A_2\\ldots A_{100}</span> be a regular <span class=\"katex--inline\">100</span>-gon with a circumcircle of diameter <span class=\"katex--inline\">1</span>. Let <span class=\"katex--inline\">M</span> be the midpoint of the minor arc <span class=\"katex--inline\">A_1A_2</span>. Find <span class=\"katex--inline\">\\sum\\limits_{i=1}^{100} |PA_i|^2</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "Problem of the Day #102", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}