{"status": "success", "data": {"description_md": "Consider a rhombus of side length $8$, with one of the acute angles being $45^\\circ$. After a $90^\\circ$ turn about the center, let the area swept out be $a+b\\pi+c\\pi\\sqrt{2}$ where $a$, $b$, $c$ are integers. Find $a+b+c$.", "description_html": "<p>Consider a rhombus of side length <span class=\"katex--inline\">8</span>, with one of the acute angles being <span class=\"katex--inline\">45^\\circ</span>. After a <span class=\"katex--inline\">90^\\circ</span> turn about the center, let the area swept out be <span class=\"katex--inline\">a+b\\pi+c\\pi\\sqrt{2}</span> where <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span>, <span class=\"katex--inline\">c</span> are integers. Find <span class=\"katex--inline\">a+b+c</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Christmas Contest - Team Round - Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/christmas1_team-p18", "prev": "/problem/christmas1_team-p16"}}