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This was the image I forgot to post yesterday. Removing the two sections from one ring, then rotating at the point where the three circles overlap will create the interlocking circle effect.

Well if you create the following shape, then get the rotation circle in the right spot you could rotate a duplicate 120, and degrees and again. But I am sure you have a more clever method.

I created a circle, increased the line width, then converted the circle to shape.

Have no idea how to do this any other way. It took me a long time just to get to this stage. :)

Over under over under over under etc.