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Clifford's circle chain theorem with n=6 circles

Following Penrose' notation, I omit letters "c" for circles and "P" for points,
to avoid cluttering.
Here we see six (n=6)
blue circles c1, c2, c3, c4, c5, c6 through O intersecting in
P12, P13, P14, P15, P23, P24, P25, P34, P35, P45, ..., P56
which again define
unique yellow circles like as c123, c125, c145, c234, c345, ..., c456.
The construction of these 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.
According to the case with
n=4
circles through O, successively taking four yellow circles at a time yields
the gold colored points P1234, P1235, P1245, P1345, P2345, ..., P3456.
The case n=5 shows that always five of these golden points
at a time, e.g. P1234, P1235, P1245, P1345, P2345 lie on red
circles c12345, etc. Alltogether there will be six such red circles c12345,
c12346, c12356, c12456, c13456, c23456. The surprising fact of the n=6 case
is, that these six red circles all coincide in the (fat violet) point P123456.

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

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

[ circle chain theorem | GA with Cinderella ]

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