{"status": "success", "data": {"description_md": "Let $ABC$ be a triangle with area $2023$. Points $D,E,F$ are constructed on $\\overline{AB}$, $\\overline{BC}$, $\\overline{CA}$, respectively, such that:\n\n$\\dfrac{AD}{DB} = \\dfrac{BE}{EC} = \\dfrac{CF}{FA} = k$\n\nfor some $k<1$. Given that $[DEF]=637$ (the area of $\\triangle DEF$) and $k$ can be written as $\\frac{a}{b}$ for relatively prime positive integers $a$ and $b$, compute the value of $100a+b$.", "description_html": "<p>Let <span class=\"katex--inline\">ABC</span> be a triangle with area <span class=\"katex--inline\">2023</span>. Points <span class=\"katex--inline\">D,E,F</span> are constructed on <span class=\"katex--inline\">\\overline{AB}</span>, <span class=\"katex--inline\">\\overline{BC}</span>, <span class=\"katex--inline\">\\overline{CA}</span>, respectively, such that:</p>&#10;<p><span class=\"katex--inline\">\\dfrac{AD}{DB} = \\dfrac{BE}{EC} = \\dfrac{CF}{FA} = k</span></p>&#10;<p>for some <span class=\"katex--inline\">k&lt;1</span>. Given that <span class=\"katex--inline\">[DEF]=637</span> (the area of <span class=\"katex--inline\">\\triangle DEF</span>) and <span class=\"katex--inline\">k</span> can be written as <span class=\"katex--inline\">\\frac{a}{b}</span> for relatively prime positive integers <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span>, compute the value of <span class=\"katex--inline\">100a+b</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "Christmas Contest - Team Round - Problem 26", "can_next": true, "can_prev": true, "nxt": "/problem/christmas1_team-p27", "prev": "/problem/christmas1_team-p25"}}