{"status": "success", "data": {"description_md": "In the complex plane, let $A$ be the set of solutions to $z^3 - 8 = 0$ and let $B$ be the set of solutions to $z^3 - 8z^2 - 8z + 64 = 0$. What is the greatest distance between a point of $A$ and a point of $B?$\n\n$\\textbf{(A) } 2\\sqrt{3} \\qquad \\textbf{(B) } 6 \\qquad \\textbf{(C) } 9 \\qquad \\textbf{(D) } 2\\sqrt{21} \\qquad \\textbf{(E) } 9 + \\sqrt{3}$\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>In the complex plane, let  <span class=\"katex--inline\">A</span>  be the set of solutions to  <span class=\"katex--inline\">z^3 - 8 = 0</span>  and let  <span class=\"katex--inline\">B</span>  be the set of solutions to  <span class=\"katex--inline\">z^3 - 8z^2 - 8z + 64 = 0</span> . What is the greatest distance between a point of  <span class=\"katex--inline\">A</span>  and a point of  <span class=\"katex--inline\">B?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } 2\\sqrt{3} \\qquad \\textbf{(B) } 6 \\qquad \\textbf{(C) } 9 \\qquad \\textbf{(D) } 2\\sqrt{21} \\qquad \\textbf{(E) } 9 + \\sqrt{3}</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": "2020 AMC 12A Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc12A_p16", "prev": "/problem/20_amc12A_p14"}}