{"status": "success", "data": {"description_md": "In the diagram, $\\triangle PQR$ is right-angled at $P$ and has $PQ = 2$ and $PR = 2\\sqrt{3}$. Altitude $PL$ intersects median $RM$ at $F$. What is the length of $PF$?\n\n<center><img class=\"problem-image\" src=\"/static/pascal/2008/crops/08_pascal_p25_fig.png\" alt=\"figure\" width=\"206\"></center>\n\n$\\text{(A)}\\ \\frac{\\sqrt{3}}{2}\\qquad\\text{(B)}\\ \\frac{3\\sqrt{3}}{7}\\qquad\\text{(C)}\\ \\frac{4\\sqrt{3}}{7}\\qquad\\text{(D)}\\ \\frac{5\\sqrt{3}}{9}\\qquad\\text{(E)}\\ \\frac{3\\sqrt{3}}{5}$\n\n___\n\n**[Pascal](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> is right-angled at <span class=\"katex--inline\">P</span> and has <span class=\"katex--inline\">PQ = 2</span> and <span class=\"katex--inline\">PR = 2\\sqrt{3}</span>. Altitude <span class=\"katex--inline\">PL</span> intersects median <span class=\"katex--inline\">RM</span> at <span class=\"katex--inline\">F</span>. What is the length of <span class=\"katex--inline\">PF</span>?</p>\n<center><img class=\"problem-image\" src=\"/static/pascal/2008/crops/08_pascal_p25_fig.png\" alt=\"figure\" width=\"206\"></center>\n<p><span class=\"katex--inline\">\\text{(A)}\\ \\frac{\\sqrt{3}}{2}\\qquad\\text{(B)}\\ \\frac{3\\sqrt{3}}{7}\\qquad\\text{(C)}\\ \\frac{4\\sqrt{3}}{7}\\qquad\\text{(D)}\\ \\frac{5\\sqrt{3}}{9}\\qquad\\text{(E)}\\ \\frac{3\\sqrt{3}}{5}</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Pascal</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": "2008 Pascal Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/08_pascal_p24"}}