{"status": "success", "data": {"description_md": "Let $a,b,$ and $c$ be real numbers such that \n\n$$a+b+c=2, \\text{ and}$$\n\n$$a^2+b^2+c^2=12$$<br>What is the difference between the maximum and minimum possible values of $c$?\n\n$\\textbf{(A) }2\\qquad \\textbf{ (B) }\\frac{10}{3}\\qquad \\textbf{ (C) }4 \\qquad \\textbf{ (D) }\\frac{16}{3}\\qquad \\textbf{ (E) }\\frac{20}{3}$\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>Let  <span class=\"katex--inline\">a,b,</span>  and  <span class=\"katex--inline\">c</span>  be real numbers such that</p>&#10;<p> <span class=\"katex--display\">a+b+c=2, \\text{ and}</span> </p>&#10;<p> <span class=\"katex--display\">a^2+b^2+c^2=12</span> <br/>What is the difference between the maximum and minimum possible values of  <span class=\"katex--inline\">c</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }2\\qquad \\textbf{ (B) }\\frac{10}{3}\\qquad \\textbf{ (C) }4 \\qquad \\textbf{ (D) }\\frac{16}{3}\\qquad \\textbf{ (E) }\\frac{20}{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": "2013 AMC 12B Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc12B_p18", "prev": "/problem/13_amc12B_p16"}}