{"status": "success", "data": {"description_md": "Let $ABCD$ be a convex quadrilateral with $BC=2$ and $CD=6.$ Suppose that the centroids of $\\triangle ABC,\\triangle BCD,$ and $\\triangle ACD$ form the vertices of an equilateral triangle. What is the maximum possible value of the area of $ABCD$?\n\n$\\textbf{(A) } 27 \\qquad\\textbf{(B) } 16\\sqrt3 \\qquad\\textbf{(C) } 12+10\\sqrt3 \\qquad\\textbf{(D) } 9+12\\sqrt3 \\qquad\\textbf{(E) } 30$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Let  <span class=\"katex--inline\">ABCD</span>  be a convex quadrilateral with  <span class=\"katex--inline\">BC=2</span>  and  <span class=\"katex--inline\">CD=6.</span>  Suppose that the centroids of  <span class=\"katex--inline\">\\triangle ABC,\\triangle BCD,</span>  and  <span class=\"katex--inline\">\\triangle ACD</span>  form the vertices of an equilateral triangle. What is the maximum possible value of the area of  <span class=\"katex--inline\">ABCD</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } 27 \\qquad\\textbf{(B) } 16\\sqrt3 \\qquad\\textbf{(C) } 12+10\\sqrt3 \\qquad\\textbf{(D) } 9+12\\sqrt3 \\qquad\\textbf{(E) } 30</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2019 AMC 12B Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/19_amc12B_p24"}}