Following Penrose' notation, I omit letters "c" for circles and "P" for points, to avoid cluttering. Here we see three (n=3) blue circles c1, c2, c3 through O intersecting in P12, P13, P23, which define the unique yellow circle c123.
The red points can be moved interactively with the mouse pointer.
Taking O to infinity changes the above into
The three blue straight lines are now three circles with infinite radius intersecting at infinity O.
Soli Deo Gloria. Created with Cinderella by Eckhard Hitzer (Fukui).