{"status": "success", "data": {"description_md": "In the diagram, $\\triangle PQR$ has $PQ = QR = RP = 30$. Points $S$ and $T$ are on $PQ$ and $PR$, respectively, so that $ST$ is parallel to $QR$. Points $V$ and $U$ are on $QR$ so that $TU$ is parallel to $PQ$ and $SV$ is parallel to $PR$. If $VS + ST + TU = 35$, the length of $VU$ is\n\n<center><img class=\"problem-image\" src=\"/static/fermat/2014/crops/14_fermat_p20_fig.png\" alt=\"figure\" width=\"358\"></center>\n\n$\\text{(A)}\\ 21\\qquad\\text{(B)}\\ 15\\qquad\\text{(C)}\\ 18\\qquad\\text{(D)}\\ 20\\qquad\\text{(E)}\\ 25$\n\n___\n\n**[Fermat](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "<p>In the diagram, <span class=\"katex--inline\">\\triangle PQR</span> has <span class=\"katex--inline\">PQ = QR = RP = 30</span>. Points <span class=\"katex--inline\">S</span> and <span class=\"katex--inline\">T</span> are on <span class=\"katex--inline\">PQ</span> and <span class=\"katex--inline\">PR</span>, respectively, so that <span class=\"katex--inline\">ST</span> is parallel to <span class=\"katex--inline\">QR</span>. Points <span class=\"katex--inline\">V</span> and <span class=\"katex--inline\">U</span> are on <span class=\"katex--inline\">QR</span> so that <span class=\"katex--inline\">TU</span> is parallel to <span class=\"katex--inline\">PQ</span> and <span class=\"katex--inline\">SV</span> is parallel to <span class=\"katex--inline\">PR</span>. If <span class=\"katex--inline\">VS + ST + TU = 35</span>, the length of <span class=\"katex--inline\">VU</span> is</p>\n<center><img class=\"problem-image\" src=\"/static/fermat/2014/crops/14_fermat_p20_fig.png\" alt=\"figure\" width=\"358\"></center>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 21\\qquad\\text{(B)}\\ 15\\qquad\\text{(C)}\\ 18\\qquad\\text{(D)}\\ 20\\qquad\\text{(E)}\\ 25</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Fermat</a>, by <a href=\"https://cemc.uwaterloo.ca/\">CEMC</a>, is licensed under the <a href=\"https://creativecommons.org/licenses/by-nc/3.0/\">CC BY-NC 3.0 DEED</a>. They are not affiliated with or endorse TopsOJ in any way.</strong></p>\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2014 Fermat Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/14_fermat_p21", "prev": "/problem/14_fermat_p19"}}