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(22)[1] in Clark Kimberling's Encyclopedia of Triangle Centers.

This was discovered in a computers-in-mathematics workshop at Phillips Exeter Academy in 1986.

[2] This is one of the recent triangle centers, unlike the classical triangle centers like centroid, incenter, and Steiner point.

[3] The Exeter point is defined as follows.

[2][4] The trilinear coordinates of the Exeter point are

a (

Reference triangle △ ABC
Medians of △ ABC ; concur at centroid
Circumcircle of △ ABC
Triangle △ A'B'C' formed by intersection of medians with circumcircle
Tangential triangle △ DEF of △ ABC
Lines joining vertices of △ DEF and △ A'B'C' ; concur at Exeter point