{"status": "success", "data": {"description_md": "Let $P$ be the convex pentagon with largest area such that all of its points lie on a semicircle with radius $1$. Denote $h_1, h_2, ... , h_5$ as the respective heights of $P$ when it is placed on each of its sides. Given that $\\sum\\limits_{i=1}^5 h_i^2 = a + \\sqrt{b}$, compute $100a+b$.", "description_html": "<p>Let <span class=\"katex--inline\">P</span> be the convex pentagon with largest area such that all of its points lie on a semicircle with radius <span class=\"katex--inline\">1</span>. Denote <span class=\"katex--inline\">h_1, h_2, ... , h_5</span> as the respective heights of <span class=\"katex--inline\">P</span> when it is placed on each of its sides. Given that <span class=\"katex--inline\">\\sum\\limits_{i=1}^5 h_i^2 = a + \\sqrt{b}</span>, compute <span class=\"katex--inline\">100a+b</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Christmas Contest - Team Round - Problem 25", "can_next": true, "can_prev": true, "nxt": "/problem/christmas1_team-p26", "prev": "/problem/christmas1_team-p24"}}