{"status": "success", "data": {"description_md": "The solutions to the equation $(z+6)^8=81$ are connected in the complex plane to form a convex regular polygon, three of whose vertices are labeled $A,B,$ and $C$. What is the least possible area of $\\triangle ABC?$\n\n$\\textbf{(A) } \\frac{1}{6}\\sqrt{6} \\qquad \\textbf{(B) } \\frac{3}{2}\\sqrt{2}-\\frac{3}{2} \\qquad \\textbf{(C) } 2\\sqrt3-3\\sqrt2 \\qquad \\textbf{(D) } \\frac{1}{2}\\sqrt{2} \\qquad \\textbf{(E) } \\sqrt 3-1$\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>The solutions to the equation  <span class=\"katex--inline\">(z+6)^8=81</span>  are connected in the complex plane to form a convex regular polygon, three of whose vertices are labeled  <span class=\"katex--inline\">A,B,</span>  and  <span class=\"katex--inline\">C</span> . What is the least possible area of  <span class=\"katex--inline\">\\triangle ABC?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } \\frac{1}{6}\\sqrt{6} \\qquad \\textbf{(B) } \\frac{3}{2}\\sqrt{2}-\\frac{3}{2} \\qquad \\textbf{(C) } 2\\sqrt3-3\\sqrt2 \\qquad \\textbf{(D) } \\frac{1}{2}\\sqrt{2} \\qquad \\textbf{(E) } \\sqrt 3-1</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": 3, "problem_name": "2018 AMC 12B Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc12B_p17", "prev": "/problem/18_amc12B_p15"}}