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Clifford's circle chain theorem with n=4 circles

Following Penrose' notation, I omit letters "c" for circles and "P" for points, to avoid cluttering. Here we see four (n=4)
blue circles c1, c2, c3, c4 through O intersecting in P12, P13, P14, P23, P24, P34
which define the four
unique yellow circle c123, c124, c134, c234. The construction of the yellow circles corresponds to applying the case
n=3
successively to three (blue) circles each, i.e. to c1,c2,c3 to give c123, etc.
The surprising fact is that the four yellow circles c123, c124, c134, c234 intersect
in one unique point P1234.
Sir R. Penrose states that this "is actually a direct consequence
of an old theorem, known to the ancient Greek geometer Appollonius" (Greece, Perge, ca. 260 - 190 BC.)

The bright red points can be moved interactively with the mouse pointer.

Taking O to infinity changes the above into

The four blue straight lines are now four circles with infinite radius intersecting at infinity O.

[ circle chain theorem | GA with Cinderella ]

Soli Deo Gloria. Created with Cinderella
by Eckhard Hitzer (Fukui).