Euclidean plane geometry

Poncelet point

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.) (Wikipedia).

Poncelet point
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From playlist Points Lines and Planes

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Related pages

Pedal triangle | Hyperbola | Cyclic quadrilateral | Geometry | Simson line | Nine-point circle | Orthocentric system