{"status": "success", "data": {"description_md": "Triangle $ABC$ is inscribed in circle $\\omega$. Points $P$ and $Q$ are on side $\\overline{AB}$ with $AP<AQ$. Rays $CP$ and $CQ$ meet $\\omega$ again at $S$ and $T$ (other than $C$), respectively. If $AP=4,PQ=3,QB=6,BT=5,$ and $AS=7$, then $ST=\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Triangle <span class=\"katex--inline\">ABC</span> is inscribed in circle <span class=\"katex--inline\">\\omega</span>. Points <span class=\"katex--inline\">P</span> and <span class=\"katex--inline\">Q</span> are on side <span class=\"katex--inline\">\\overline{AB}</span> with <span class=\"katex--inline\">AP&lt;AQ</span>. Rays <span class=\"katex--inline\">CP</span> and <span class=\"katex--inline\">CQ</span> meet <span class=\"katex--inline\">\\omega</span> again at <span class=\"katex--inline\">S</span> and <span class=\"katex--inline\">T</span> (other than <span class=\"katex--inline\">C</span>), respectively. If <span class=\"katex--inline\">AP=4,PQ=3,QB=6,BT=5,</span> and <span class=\"katex--inline\">AS=7</span>, then <span class=\"katex--inline\">ST=\\frac{m}{n}</span>, where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime positive integers. Find <span class=\"katex--inline\">m+n</span>.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2016 AIME II Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/16_aime_II_p11", "prev": "/problem/16_aime_II_p09"}}