Miquelian inversive plane

Definition
An inversive plane is said to be 'Miquelian'' if it satisfies the following. Let $$C_1, C_2, C_3, C_4$$ be four circles and let the intersection of $$C_i$$ with $$C_{i+1}$$ (read modulo 4) be the set $$\{ a_i,b_i \}$$ ($$a_i$$ may be equal to $$b_i$$). Then, $$a_i$$s are concircular if and only if the $$b_i$$s are concircular.

It turns out that an inversive plane is Miquelian if and only if it arises from a non-ruled quadric in a three-dimensional geometry over a commutative field.

Weaker properties

 * Inversive plane satisfying bundle theorem