![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Poncelet_point.svg/640px-Poncelet_point.svg.png&w=640&q=50)
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:
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Poncelet_point.svg/320px-Poncelet_point.svg.png)
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.)