{"status": "success", "data": {"description_md": "Let $c$ be a real number, and let $z_1$ and $z_2$ be the two complex numbers satisfying the equation\n\n$z^2 - cz + 10 = 0$. Points $z_1$, $z_2$, $\\frac{1}{z_1}$, and $\\frac{1}{z_2}$ are the vertices of (convex) quadrilateral $\\mathcal{Q}$ in the complex plane. When the area of $\\mathcal{Q}$ obtains its maximum possible value, $c$ is closest to which of the following?\n\n$\\textbf{(A) }4.5 \\qquad\\textbf{(B) }5 \\qquad\\textbf{(C) }5.5 \\qquad\\textbf{(D) }6\\qquad\\textbf{(E) }6.5$\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\">c</span>  be a real number, and let  <span class=\"katex--inline\">z_1</span>  and  <span class=\"katex--inline\">z_2</span>  be the two complex numbers satisfying the equation</p>&#10;<p> <span class=\"katex--inline\">z^2 - cz + 10 = 0</span> . Points  <span class=\"katex--inline\">z_1</span> ,  <span class=\"katex--inline\">z_2</span> ,  <span class=\"katex--inline\">\\frac{1}{z_1}</span> , and  <span class=\"katex--inline\">\\frac{1}{z_2}</span>  are the vertices of (convex) quadrilateral  <span class=\"katex--inline\">\\mathcal{Q}</span>  in the complex plane. When the area of  <span class=\"katex--inline\">\\mathcal{Q}</span>  obtains its maximum possible value,  <span class=\"katex--inline\">c</span>  is closest to which of the following?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }4.5 \\qquad\\textbf{(B) }5 \\qquad\\textbf{(C) }5.5 \\qquad\\textbf{(D) }6\\qquad\\textbf{(E) }6.5</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": "2022 AMC 12A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc12A_p23", "prev": "/problem/22_amc12A_p21"}}