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 `(4/3)*tan(pi/(2n))`

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So for 4 points it is `(4/3)*tan(pi/8) = 4*(sqrt(2)-1)/3 = 0.552284749831`

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