Clifford's Circle Theorem


Let C_1, C_2, C_3, and C_4 be four circles of general position through a point P. Let P_(ij) be the second intersection of the circles C_i and C_j. Let C_(ijk) be the circle P_(ij)P_(ik)P_(jk). Then the four circles C_(234), C_(134), C_(124), and C_(123) all pass through the point P_(1234). Similarly, let C_5 be a fifth circle through P. Then the five points P_(2345), P_(1345), P_(1245), P_(1235) and P_(1234) all lie on one circle C_(12345). And so on.

See also

Circle, Cox's Theorem

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Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 32-33, 1991.

Referenced on Wolfram|Alpha

Clifford's Circle Theorem

Cite this as:

Weisstein, Eric W. "Clifford's Circle Theorem." From MathWorld--A Wolfram Web Resource.

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