Poncelet point
Intersection of the 9-point circles of all triangles made from 4 points / From Wikipedia, the free encyclopedia
In geometry, the Poncelet point of four given points is defined as follows:
Let A, B, C, 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, △DAB meet at one point, the Poncelet point of the points A, B, C, D. (If A, B, C, 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.)