Check the picture below.
if we know the endpoints of the circle, then its center must be the midpoint of those two endpoints.
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{-2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{10-6}{2}~~,~~\cfrac{-2+2}{2} \right)\implies \left( \cfrac{4}{2}~~,~~\cfrac{0}{2} \right)\implies (2~~,~~0)[/tex]
