I need to draw a circle in 45 degree angle sections instead of the easier 90 degree. So there would be 8 curveTo's instead of 4.

This code shows the 4 curveTo way:
Code:
this.createEmptyMovieClip("test",3);
with(this.test) {
  clear();
  var x = 10;
  var y = 10;
  var radius = 10;
  beginFill( 0xCCCCCC );
  lineStyle( 1, 0x000000, 30 );
  moveTo(x,y + radius );
  //var smallSide = (curveDepth-Math.sqrt((Math.pow(curveDepth,2)/2)))-(curveDepth/100);
  curveTo( x+1, y+halfCurve, x + smallSide, y+smallSide);
  curveTo( x, y+radius , x + radius , y+radius );
  curveTo( x + (radius *2), y, x + (radius *2), y + radius );
  curveTo( x + (radius *2, y + (radius *2), x + radius , y + (radius *2) );
  curveTo( x, y + (radius *2), x, y + radius );
  endFill();
}
I want to have 8 curveTo's and have it still look like a perfect circle.
Of course the code needs to handle any size of radius.

Thanks in advance for anyone that comes up with the cooridnates i need.