Concentric circles in inversive-geometry Is it possible to obtain two concentric generalised circles(parallel straight lines) through inversion of two circles w.r.t a third circle?

![ParallelInvrsns](

Some parallel line segments are shown reflected about a unit circle centered at origin as mirror ( feature available in _Geogebra_ ). When parallel lines go to $ \infty,$ then their images inside the inversion circle tend to go to the origin, being tangent only at an infinite distance from the farthest points .. a feature of hyperbolic geometry. The images can never be concentric just as in both the Poincare's models ( semi-infinite plane or disk.)

EDIT 1:

![nvesnParllLines](

Inversions of a set of parallel lines bear same label in the figure above.

A set of parallel lines have _co-tangential_ circular inversions.

These inversions have either to be _co-tangential_ or _con-centric_ but _not both_ at the same time !!