{"status": "success", "data": {"description_md": "Given a regular $16$-gon $ABCDEFGHIJKLMNOP$, with $AI=8$, the area of $ABEF$ can be written as $\\sqrt{a - b\\sqrt c}$ where $a$, $b$, and $c$ are positive integers where $c$ is not divisible by the square of any prime. Find $a + b + c$.", "description_html": "<p>Given a regular <span class=\"katex--inline\">16</span>-gon <span class=\"katex--inline\">ABCDEFGHIJKLMNOP</span>, with <span class=\"katex--inline\">AI=8</span>, the area of <span class=\"katex--inline\">ABEF</span> can be written as <span class=\"katex--inline\">\\sqrt{a - b\\sqrt c}</span> where <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span>, and <span class=\"katex--inline\">c</span> are positive integers where <span class=\"katex--inline\">c</span> is not divisible by the square of any prime. Find <span class=\"katex--inline\">a + b + c</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "Grinding Aces Math Exam 2025 - Problem 10", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}