Clifford’s chain of theorems in affine CK-planes

In [H. Martini, M. Spirova, Circle geometry in affine Cayley-Klein planes, Periodica Mathematica Hungarica 57 (2) (2008) 197 – 206.], certain new properties of circles related to the analogues of the Clifford’s chain of theorems are presented in affine CK-planes. After the first analogue was made, the authors conclude that unfortunately the next step of the Clifford’s chain cannot be analogously extended to the affine CK-planes. In this article, by presenting and proving all analogues of the Clifford’s chain of theorems in the affine CK-plane, we prove contrary