  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.
