{"status": "success", "data": {"description_md": "**POTD February 29, 2024**\n\n$ABCD$ is a parallelogram satisfying $AB = 7, BC = 2$, and $\\angle DAB = 120^\\circ{}$. Parallelogram $ECFA$ is contained in $ABCD$ and is similar to it. If the ratio of the area of $ECFA$ to the area of $ABCD$ can be written as a fraction $\\frac{m}{n},$ where $m,n$ are relatively prime positive integers, find $m+n$.", "description_html": "<p><strong>POTD February 29, 2024</strong></p>&#10;<p><span class=\"katex--inline\">ABCD</span> is a parallelogram satisfying <span class=\"katex--inline\">AB = 7, BC = 2</span>, and <span class=\"katex--inline\">\\angle DAB = 120^\\circ{}</span>. Parallelogram <span class=\"katex--inline\">ECFA</span> is contained in <span class=\"katex--inline\">ABCD</span> and is similar to it. If the ratio of the area of <span class=\"katex--inline\">ECFA</span> to the area of <span class=\"katex--inline\">ABCD</span> can be written as a fraction <span class=\"katex--inline\">\\frac{m}{n},</span> where <span class=\"katex--inline\">m,n</span> are relatively prime positive integers, find <span class=\"katex--inline\">m+n</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #82", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}