{"status": "success", "data": {"description_md": "Consider a line segment $AC$ with a point $B$ between $A$ and $C$ such that $AB = 12$. Circle $\\gamma$ is drawn with diameter $AB$, and the tangent from point $C$ to $\\gamma$ is tangent at a point $X$. Let $Y$ denote the foot of the perpendicular from $B$ to $XC$. Find the maximum possible value of $AY$.", "description_html": "<p>Consider a line segment <span class=\"katex--inline\">AC</span> with a point <span class=\"katex--inline\">B</span> between <span class=\"katex--inline\">A</span> and <span class=\"katex--inline\">C</span> such that <span class=\"katex--inline\">AB = 12</span>. Circle <span class=\"katex--inline\">\\gamma</span> is drawn with diameter <span class=\"katex--inline\">AB</span>, and the tangent from point <span class=\"katex--inline\">C</span> to <span class=\"katex--inline\">\\gamma</span> is tangent at a point <span class=\"katex--inline\">X</span>. Let <span class=\"katex--inline\">Y</span> denote the foot of the perpendicular from <span class=\"katex--inline\">B</span> to <span class=\"katex--inline\">XC</span>. Find the maximum possible value of <span class=\"katex--inline\">AY</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #64", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}