{"status": "success", "data": {"description_md": "**POTD Challenge December 12, 2023**\n**Author:** awesomeming327\n\nConsider a circle $\\omega$ of radius $3$ with center $O$ and a point $P$ outside such that $OP=5$. Let the tangents from $P$ to $\\omega$ meet $\\omega$ at $A$ and $B$. Consider a point $X$ on the minor arc $AB$, and let the circumcircle of $POX$ meet $\\omega$ again at $Y$. Let $XY$ intersect $AB$ at $Q$. If $XQ = \\frac{4}{9}YQ$, and $XY = \\frac{m}{n}$, find the value of $m+n$.", "description_html": "<p><strong>POTD Challenge December 12, 2023</strong><br/>&#10;<strong>Author:</strong> awesomeming327</p>&#10;<p>Consider a circle <span class=\"katex--inline\">\\omega</span> of radius <span class=\"katex--inline\">3</span> with center <span class=\"katex--inline\">O</span> and a point <span class=\"katex--inline\">P</span> outside such that <span class=\"katex--inline\">OP=5</span>. Let the tangents from <span class=\"katex--inline\">P</span> to <span class=\"katex--inline\">\\omega</span> meet <span class=\"katex--inline\">\\omega</span> at <span class=\"katex--inline\">A</span> and <span class=\"katex--inline\">B</span>. Consider a point <span class=\"katex--inline\">X</span> on the minor arc <span class=\"katex--inline\">AB</span>, and let the circumcircle of <span class=\"katex--inline\">POX</span> meet <span class=\"katex--inline\">\\omega</span> again at <span class=\"katex--inline\">Y</span>. Let <span class=\"katex--inline\">XY</span> intersect <span class=\"katex--inline\">AB</span> at <span class=\"katex--inline\">Q</span>. If <span class=\"katex--inline\">XQ = \\frac{4}{9}YQ</span>, and <span class=\"katex--inline\">XY = \\frac{m}{n}</span>, find the value of <span class=\"katex--inline\">m+n</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "Problem of the Day #23 (Challenge)", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}