{"status": "success", "data": {"description_md": "**POTD January 11, 2024**\n\nIn a circle $\\Omega$ of radius $9$, draw a diameter, and two parallel and congruent chords of the circle that intersect the diameter such that there exist circles of radius $4$ tangent to both chords, the diameter, and internally tangent to $\\omega$. Let $\\omega$ be the acute angle formed by the intersection of a chord with the diameter. If $\\tan(\\omega)$ can be expressed as $\\frac{a}{b}$, where $a$ and $b$ are positive, relatively prime, integers, find $a+b$.", "description_html": "<p><strong>POTD January 11, 2024</strong></p>&#10;<p>In a circle <span class=\"katex--inline\">\\Omega</span> of radius <span class=\"katex--inline\">9</span>, draw a diameter, and two parallel and congruent chords of the circle that intersect the diameter such that there exist circles of radius <span class=\"katex--inline\">4</span> tangent to both chords, the diameter, and internally tangent to <span class=\"katex--inline\">\\omega</span>. Let <span class=\"katex--inline\">\\omega</span> be the acute angle formed by the intersection of a chord with the diameter. If <span class=\"katex--inline\">\\tan(\\omega)</span> can be expressed as <span class=\"katex--inline\">\\frac{a}{b}</span>, where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are positive, relatively prime, integers, find <span class=\"katex--inline\">a+b</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #37", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}