{"status": "success", "data": {"description_md": "**POTD March 9, 2024**\n\nA rectangle with height $2$ and length $4\\sqrt{3}$ is inscribed in a semicircle with the diameter touching the rectangle\u2019s longer side by. Let $x$ be the area of the the sector formed by the intersection of the rectangle and circle. If $\\frac{x}{\\pi} = \\frac{a}{b}$, where $a$ and $b$ are relatively prime, positive integers, find $a+b$.", "description_html": "<p><strong>POTD March 9, 2024</strong></p>&#10;<p>A rectangle with height <span class=\"katex--inline\">2</span> and length <span class=\"katex--inline\">4\\sqrt{3}</span> is inscribed in a semicircle with the diameter touching the rectangle&#8217;s longer side by. Let <span class=\"katex--inline\">x</span> be the area of the the sector formed by the intersection of the rectangle and circle. If <span class=\"katex--inline\">\\frac{x}{\\pi} = \\frac{a}{b}</span>, where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are relatively prime, positive integers, find <span class=\"katex--inline\">a+b</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "Problem of the Day #91", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}