{"status": "success", "data": {"description_md": "Let $ABC$ be a triangle with $AB=16$, $CA=11$, $BC=7$. The incircle touches $AB$ and $BC$ at $F$ and $D$, respectively. Let $X$ be a point on segment $AF$ and let $DX$ intersect $CF$ at $G$. Let $BG$ and $AC$ intersect at $H$. $XH$ is parallel to $FC$. Let $HC$ be $\\tfrac{a}{b}$ where $a$ and $b$ are relatively prime positive integers. Find $a+b$.", "description_html": "<p>Let <span class=\"katex--inline\">ABC</span> be a triangle with <span class=\"katex--inline\">AB=16</span>, <span class=\"katex--inline\">CA=11</span>, <span class=\"katex--inline\">BC=7</span>. The incircle touches <span class=\"katex--inline\">AB</span> and <span class=\"katex--inline\">BC</span> at <span class=\"katex--inline\">F</span> and <span class=\"katex--inline\">D</span>, respectively. Let <span class=\"katex--inline\">X</span> be a point on segment <span class=\"katex--inline\">AF</span> and let <span class=\"katex--inline\">DX</span> intersect <span class=\"katex--inline\">CF</span> at <span class=\"katex--inline\">G</span>. Let <span class=\"katex--inline\">BG</span> and <span class=\"katex--inline\">AC</span> intersect at <span class=\"katex--inline\">H</span>. <span class=\"katex--inline\">XH</span> is parallel to <span class=\"katex--inline\">FC</span>. Let <span class=\"katex--inline\">HC</span> be <span class=\"katex--inline\">\\tfrac{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": 8, "problem_name": "TxO Math Bowl 2024 - Guts Contest - Set 9 Problem 2", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}