{"status": "success", "data": {"description_md": "In $\\triangle TXO$, points $G$ and $L$ are on sides $TO$ and $XO$, respectively, and points $E$ and $B$ are on side $TX$ with $E$ closer to $X$. Cevians $OB$ and $XG$ intersect at $P$, and $XG$ intersects transversal $EL$ at $Q$. As well, $BE=3, TG=TB=XL=LO=6,$ and $EX=OG=9$. If the value of $\\frac{QX}{PG}$ can be expressed as $\\frac{a}{b}$, where $a$ and $b$ are relatively prime, positive integers, compute $a+b$.", "description_html": "<p>In <span class=\"katex--inline\">\\triangle TXO</span>, points <span class=\"katex--inline\">G</span> and <span class=\"katex--inline\">L</span> are on sides <span class=\"katex--inline\">TO</span> and <span class=\"katex--inline\">XO</span>, respectively, and points <span class=\"katex--inline\">E</span> and <span class=\"katex--inline\">B</span> are on side <span class=\"katex--inline\">TX</span> with <span class=\"katex--inline\">E</span> closer to <span class=\"katex--inline\">X</span>. Cevians <span class=\"katex--inline\">OB</span> and <span class=\"katex--inline\">XG</span> intersect at <span class=\"katex--inline\">P</span>, and <span class=\"katex--inline\">XG</span> intersects transversal <span class=\"katex--inline\">EL</span> at <span class=\"katex--inline\">Q</span>. As well, <span class=\"katex--inline\">BE=3, TG=TB=XL=LO=6,</span> and <span class=\"katex--inline\">EX=OG=9</span>. If the value of <span class=\"katex--inline\">\\frac{QX}{PG}</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 relatively prime, positive integers, compute <span class=\"katex--inline\">a+b</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "TxO Math Bowl 2024 - Team Contest - Problem 3", "can_next": true, "can_prev": true, "nxt": "/problem/txo2024team-p04", "prev": "/problem/txo2024team-p02"}}