As already said: there is no exact representation of the circle using Bezier curves.
To complete the other answers : for Bezier curve with
n segments the optimal distance to the control points, in the sense that the middle of the curve lies on the circle itself, is
So for 4 points it is
(4/3)*tan(pi/8) = 4*(sqrt(2)-1)/3 = 0.552284749831.