{"status": "success", "data": {"description_md": "**POTD April 14, 2024**\n\nLet $A_1,A_2,\\ldots, A_{2020}$ be a regular $2020-\\text{gon}$ with a circumcircle $C$ of diameter $1$. Now let $P$ be the midpoint of the minor-arc $A_1A_2$ on circumcircle $C$. Find $\\sum\\limits_{i=1}^{2020} |PA_i|^2$", "description_html": "<p><strong>POTD April 14, 2024</strong></p>&#10;<p>Let <span class=\"katex--inline\">A_1,A_2,\\ldots, A_{2020}</span> be a regular <span class=\"katex--inline\">2020-\\text{gon}</span> with a circumcircle <span class=\"katex--inline\">C</span> of diameter <span class=\"katex--inline\">1</span>. Now let <span class=\"katex--inline\">P</span> be the midpoint of the minor-arc <span class=\"katex--inline\">A_1A_2</span> on circumcircle <span class=\"katex--inline\">C</span>. Find <span class=\"katex--inline\">\\sum\\limits_{i=1}^{2020} |PA_i|^2</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #127", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}