The same construction works to form two circles inside a third, but you should use two external bisectors and one internal bisector instead of three internal bisectors. (Curious fact: three bisectors meet iff the number of external ones is even.) If you move the anchor points in the animation around, you may be able to reach a configuration like this.
Similarly to this pattern, four tangent circles also always have a circle through their tangencies, but it is not always perpendicular to them.
Animation created by Cinderella.
From the Geometry Junkyard, computational and recreational geometry.
David Eppstein, Theory Group, ICS, UC Irvine.
Last update: .