Following Penrose' notation, I omit letters "c" for circles and "P" for points, to avoid cluttering. Here we see two (n=2) circles c1, c2 through O intersecting in P12.
The red points can be moved interactively with the mouse pointer.
Taking O to infinity changes the above into
The two blue straight lines are now two circles with infinite radius also intersecting at infinity O.
Soli Deo Gloria. Created with Cinderella by Eckhard Hitzer (Fukui).