Exeter point
In geometry , the Exeter point is one of the excellent points of a plane triangle . The Exeter Point has the designation X in Clark Kimberling's Encyclopedia of Triangle Centers (22). The point was discovered at a Phillips Exeter Academy computational math workshop in 1986. This makes it one of the triangular centers that have recently been found - in contrast to the classic points such as the center of gravity , the incircle center or the Steiner point .
definition
The Exeter point is defined as follows:
- Let an arbitrary triangle ABC be given. The points of intersection of the extended bisector with the circumference are denoted by A ' , B' and C ' . DEF is the triangle that is formed by the tangents to the circumference at points A , B and C ( D opposite A , E opposite B and F opposite C ). Then the straight lines DA ' , EB' and FC ' intersect at a point. This intersection is the Exeter point of triangle ABC .
Trilinear and barycentric coordinates
The trilinear coordinates of the Exeter point are
properties
- The Exeter point of triangle ABC lies on the Euler straight line of triangle ABC (the line that goes through the center of gravity , the vertical intersection and the circumcenter ).
Individual evidence
- ^ Clark Kimberling: Encyclopedia of Triangle Centers: X (22) . Retrieved January 14, 2017.
- ^ A b Clark Kimberling: Exeter Point . Retrieved January 14, 2017.
- ^ Clark Kimberling: Triangle centers . Retrieved January 14, 2017.
- ↑ Eric W. Weisstein: Exeter Point . From MathWorld - A Wolfram Web Resource. Retrieved January 14, 2017.