Orthogonality related to Steiner and Pappus chains

The focus of this paper is on the study of specific circle formations known as orthogonal Pappus chains and the related incidence results that involve points of tangency between the circles in the construction. These chains give rise to new circle families, with their centres on a conic. The paper also explores similar questions for Steiner chains, although it is demonstrated that orthogonality cannot be defined for them. Nonetheless, explicit examples are provided, exhibiting comparable incidence results and raising whether two Steiner chains that share a common circle in the chains possess this property