{"status": "success", "data": {"description_md": "Let $\\triangle ABC$ be an isosceles triangle with $AB = AC$. Let $\\gamma$ denote the arc $CAB$ of the circumcircle of $\\triangle ABC$ and let $\\gamma'$ be the reflection of $\\gamma$ across $BC$. Let $I$ be the center of the circle tangent to $AB$, $AC$, and internally tangent to $\\gamma'$. Let $D$ be the midpoint of $AI$. Given that $\\angle ADC = 97^\\circ$, find $\\angle CAB$ in degrees.", "description_html": "<p>Let <span class=\"katex--inline\">\\triangle ABC</span> be an isosceles triangle with <span class=\"katex--inline\">AB = AC</span>. Let <span class=\"katex--inline\">\\gamma</span> denote the arc <span class=\"katex--inline\">CAB</span> of the circumcircle of <span class=\"katex--inline\">\\triangle ABC</span> and let <span class=\"katex--inline\">\\gamma'</span> be the reflection of <span class=\"katex--inline\">\\gamma</span> across <span class=\"katex--inline\">BC</span>. Let <span class=\"katex--inline\">I</span> be the center of the circle tangent to <span class=\"katex--inline\">AB</span>, <span class=\"katex--inline\">AC</span>, and internally tangent to <span class=\"katex--inline\">\\gamma'</span>. Let <span class=\"katex--inline\">D</span> be the midpoint of <span class=\"katex--inline\">AI</span>. Given that <span class=\"katex--inline\">\\angle ADC = 97^\\circ</span>, find <span class=\"katex--inline\">\\angle CAB</span> in degrees.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 7, "problem_name": "Holiday Contest 2025 - Team Round - Problem 18", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}