I'm still stumped. Isn't this an 'origin circle' then? Radius == the pt-pt distance.

http://www.sciencevsmagic.net/geo/#0A1.1A0.2A0.0L2.2L7.4L1.1...

Scratch that - the same thing works if rotated:

http://www.sciencevsmagic.net/geo/#1A0.0A1.2A0.1L5.2L0.0L9.9...