Here is a construction you can play with:

With the Ellipse Tool, hold the Ctrl key down and with the Radius or Diameter constraint, draw a red 200 pt circle with zero rotation.
Clone it and colour it green.
With the green circle still selected, switch to the QuickShape Tool and select a Polygon with 8 straight sides.
You should now have a green octogon sitting inside a red circle.

Click drag the centre point of one of the edges radially outwards so it touches the circle circumference.
You should now have a green rounded QuckShape coincident with your red circle.

Delete the red circle.
Clone the green shape.
Use Combine Shapes > Add Shapes to get a final Shape with 8 control points that are equidistant and looks like a green circle.

Acorn