{"status": "success", "data": {"description_md": "In equilateral triangle $PQR$, $S$ is the midpoint of $PR$, $T$ is on $PQ$ so that $PT = 1$ and $TQ = 3$. Many circles can be drawn inside quadrilateral $QRST$ so that no part extends outside of $QRST$. The radius of the largest such circle is closest to\n\n<center><img class=\"problem-image\" src=\"/static/fermat/2012/crops/12_fermat_p24_fig.png\" alt=\"figure\" width=\"370\"></center>\n\n$\\text{(A)}\\ 1.00\\qquad\\text{(B)}\\ 1.10\\qquad\\text{(C)}\\ 1.15\\qquad\\text{(D)}\\ 1.05\\qquad\\text{(E)}\\ 1.37$\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 equilateral triangle <span class=\"katex--inline\">PQR</span>, <span class=\"katex--inline\">S</span> is the midpoint of <span class=\"katex--inline\">PR</span>, <span class=\"katex--inline\">T</span> is on <span class=\"katex--inline\">PQ</span> so that <span class=\"katex--inline\">PT = 1</span> and <span class=\"katex--inline\">TQ = 3</span>. Many circles can be drawn inside quadrilateral <span class=\"katex--inline\">QRST</span> so that no part extends outside of <span class=\"katex--inline\">QRST</span>. The radius of the largest such circle is closest to</p>\n<center><img class=\"problem-image\" src=\"/static/fermat/2012/crops/12_fermat_p24_fig.png\" alt=\"figure\" width=\"370\"></center>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 1.00\\qquad\\text{(B)}\\ 1.10\\qquad\\text{(C)}\\ 1.15\\qquad\\text{(D)}\\ 1.05\\qquad\\text{(E)}\\ 1.37</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": "2012 Fermat Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/12_fermat_p25", "prev": "/problem/12_fermat_p23"}}