{"status": "success", "data": {"description_md": "A unit square is drawn with vertices $A,B,C,D.$ Denote the midpoint of side $AD$ by $E$ and the midpoint of side $BE$ as $F$. Let the area of quadrilateral $DFBC$ be $\\tfrac{a}{b}$ where $\\gcd(a,b)=1$. Find $100a+b$", "description_html": "<p>A unit square is drawn with vertices <span class=\"katex--inline\">A,B,C,D.</span> Denote the midpoint of side <span class=\"katex--inline\">AD</span> by <span class=\"katex--inline\">E</span> and the midpoint of side <span class=\"katex--inline\">BE</span> as <span class=\"katex--inline\">F</span>. Let the area of quadrilateral <span class=\"katex--inline\">DFBC</span> be <span class=\"katex--inline\">\\tfrac{a}{b}</span> where <span class=\"katex--inline\">\\gcd(a,b)=1</span>. Find <span class=\"katex--inline\">100a+b</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "Christmas Contest - Team Round - Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/christmas1_team-p08", "prev": "/problem/christmas1_team-p06"}}