Some theorems from inversive and Euclidean circle geometry are extended to all affine Cayley-Klein planes. In particular,
we obtain an analogue to the first step of Clifford’s chain of theorems, a statement related to Napoleon’s theorem, extensions
of Wood’s theorem on similar-perspective triangles and of the known fact that the three radical axes of three given circles
are parallel or have a point in common. For proving these statements, we use generalized complex numbers.