Exeter point


In geometry, the Exeter point is a special point associated with a plane triangle. It is a triangle center and is designated as X 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, unlike the classical triangle centers like centroid, incenter, and Steiner point.

Definition

The Exeter point is defined as follows.
Put succinctly, the Exeter point is the perspector of the circummedial triangle and the tangential triangle.

Trilinear coordinates

The trilinear coordinates of the Exeter point are

Properties