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. The nine-point circles of triangles ABC, BCD, CDA, DAB meet at one point, the Poncelet point of the points A, B, C, and D. If A, B, C, and D be four points in the plane that form an orthocentric system then triangles ABC, BCD, CDA, DAB all share the same nine-point circle.