AMC 12B 2013 Problem 17

Let a, b, and c be real numbers such that

\left\{\begin{array}{l} a+b+c=2, \text { and } \\ a^{2}+b^{2}+c^{2}=12 \end{array}\right.

What is the difference between the maximum and minimum possible values of c ?

Answer Choices
A. 2
B. \dfrac{10}{3}
C. 4
D. \dfrac{16}{3}
E. \dfrac{20}{3}