Determine the Real Solutions to the System of Nonlinear Equations $$\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 50 \\( x - 2 ) ^ { 2 } + y ^ { 2 } = 50\end{array}$$

Multiple Choice

Determine the real solutions to the system of nonlinear equations.
- $$\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 50 \\( x - 2 ) ^ { 2 } + y ^ { 2 } = 50\end{array}$$

A) $( 1,7 ) , ( 1 , - 7 ) , ( - 1,7 ) , ( - 1 , - 7 )$
B) $( 7,1 ) , ( 7 , - 1 )$
C) $( 7,1 ) , ( 7 , - 1 ) , ( - 7,1 ) , ( - 7 , - 1 )$
D) $( 1,7 ) , ( 1 , - 7 )$