{"status": "success", "data": {"description_md": "The area of $\\bigtriangleup ABC$ is $1$. As shown in the figure, $D$ and $E$ trisect $BC$. $F$ and $G$ trisect $CA$. Find the area of quadrilateral $PECF$.\n\nIf the answer is $\\frac{a}{b}$, where $a$ and $b$ are relatively prime, positive integers, input $a^b+2ab+b^a$.\n\n<img src=\"/static/geo1.png\" width=\"600px\">", "description_html": "<p>The area of <span class=\"katex--inline\">\\bigtriangleup ABC</span> is <span class=\"katex--inline\">1</span>. As shown in the figure, <span class=\"katex--inline\">D</span> and <span class=\"katex--inline\">E</span> trisect <span class=\"katex--inline\">BC</span>. <span class=\"katex--inline\">F</span> and <span class=\"katex--inline\">G</span> trisect <span class=\"katex--inline\">CA</span>. Find the area of quadrilateral <span class=\"katex--inline\">PECF</span>.</p>&#10;<p>If the answer is <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, input <span class=\"katex--inline\">a^b+2ab+b^a</span>.</p>&#10;<img src=\"/static/geo1.png\" width=\"600px\"/>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Geometry Practice #1", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}