Before revision:  We also have some additional examples of non-circularizable arrangements of 6 pseudocircles . The proofs of non-circularizability use various techniques, most depend on incidence theorems , others use arguments involving metric properties of arrangements of planes, or angles in planar figures .
After revision:  We also have some additional examples of non-circularizable arrangements of 6 pseudocircles are non-circularizable. Most of our non-circularizability use various techniques, most depend on incidence theorems , others use arguments involving metric properties of arrangements of planes, or angles in planar figures .