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About: Poncelet point     Goto   Sponge   NotDistinct   Permalink

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In geometry, the Poncelet point of four given points is defined as follows: Let A, B, C, and D be four points in the plane that do not form an orthocentric system and such that no three of them are collinear. The nine-point circles of triangles ABC, BCD, CDA, and DAB meet at one point, the Poncelet point of the points A, B, C, and D. (If A, B, C, and D do form an orthocentric system, then triangles ABC, BCD, CDA, DAB all share the same nine-point circle, and the Poncelet point is undefined.)