Exeter point

In geometry, the Exeter point is a special point associated with a plane triangle. The Exeter point is a triangle center and is designated as the center X(22) in Clark Kimberling's Encyclopedia of Triangle Centers. This was discovered in a computers-in-mathematics workshop at Phillips Exeter Academy in 1986. This is one of the recent triangle centers, having been discovered only in 1986, unlike the classical triangle centers like centroid, incenter, and Steiner point.

The Exeter point is defined as follows.

The trilinear coordinates of the Exeter point are