the perpendicular bisectors of the 3 sides will meet at the centre of the circle.
midpoint of EF will be (4+4)2 , (4+2)/2 = (4,3)
equation of EF is x = 4 so the equation of the line perpendicular to EF will be
y = 3
midpoint of FG is (6,2) so line perpendicualr to it is x = 6
so center of the circle is ( 6 , 3)