# Category: Triangle centers

Equal parallelians point
In geometry, the equal parallelians point (also called congruent parallelians point) is a special point associated with a plane triangle. It is a triangle center and it is denoted by X(192) in Clark K
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 Tri
Lemoine point
In geometry, the symmedian point, Lemoine point or Grebe point is the intersection of the three symmedians (medians reflected at the associated angle bisectors) of a triangle. Ross Honsberger called i
Encyclopedia of Triangle Centers
The Encyclopedia of Triangle Centers (ETC) is an online list of thousands of points or "centers" associated with the geometry of a triangle. It is maintained by Clark Kimberling, Professor of Mathemat
Apollonius point
In triangle geometry, the Apollonius point is a special point associated with a plane triangle. The point is a triangle center and it is designated as X(181) in Clark Kimberling's Encyclopedia of Tria
Nagel point
In geometry, the Nagel point is a triangle center, one of the points associated with a given triangle whose definition does not depend on the placement or scale of the triangle. The Nagel point is nam
Yff center of congruence
In geometry, the Yff center of congruence is a special point associated with a triangle. This special point is a triangle center and Peter Yff initiated the study of this triangle center in 1987.
Steiner point (triangle)
In triangle geometry, the Steiner point is a particular point associated with a triangle. It is a triangle center and it is designated as the center X(99) in Clark Kimberling's Encyclopedia of Triangl
Schiffler point
In geometry, the Schiffler point of a triangle is a triangle center, a point defined from the triangle that is equivariant under Euclidean transformations of the triangle. This point was first defined
Symmedian point
No description available.
Trisected perimeter point
In geometry, given a triangle ABC, there exist unique points A´, B´, and C´ on the sides BC, CA, AB respectively, such that: * A´, B´, and C´ partition the perimeter of the triangle into three equal-
Nine-point center
In geometry, the nine-point center is a triangle center, a point defined from a given triangle in a way that does not depend on the placement or scale of the triangle.It is so called because it is the
Vecten points
In the geometry of triangles, the Vecten points are two triangle centers associated with any triangle. They may be constructed by constructing three squares on the sides of the triangle, connecting ea
Triangle center
In geometry, a triangle center (or triangle centre) is a point in the plane that is in some sense a center of a triangle akin to the centers of squares and circles, that is, a point that is in the mid
Clawson point
The Clawson point is a special point in a planar triangle defined by the trilinear coordinates (Kimberling number X(19)), where are the interior angles at the triangle vertices . It is named after , w
Incenter
In geometry, the incenter of a triangle is a triangle center, a point defined for any triangle in a way that is independent of the triangle's placement or scale. The incenter may be equivalently defin
Circumcenter
No description available.
Mittenpunkt
In geometry, the mittenpunkt (German, middlespoint) of a triangle is a triangle center: a point defined from the triangle that is invariant under Euclidean transformations of the triangle. It was iden
Isoperimetric point
In geometry, the isoperimetric point is a special point associated with a plane triangle. The term was originally introduced by G.R. Veldkamp in a paper published in the American Mathematical Monthly
Isodynamic point
In Euclidean geometry, the isodynamic points of a triangle are points associated with the triangle, with the properties that an inversion centered at one of these points transforms the given triangle
Bevan point
The Bevan point, named after Benjamin Bevan, is a triangle center. It is defined as center of the Bevan circle, that is the circle through the centers of the three excircles of a triangle. The Bevan p
Parry point (triangle)
In geometry, the Parry point is a special point associated with a plane triangle. It is the triangle center designated X(111) in Clark Kimberling's Encyclopedia of Triangle Centers. The Parry point an
Kosnita point
No description available.
Gossard perspector
In geometry the Gossard perspector (also called the Zeeman–Gossard perspector) is a special point associated with a plane triangle. It is a triangle center and it is designated as X(402) in Clark Kimb
Congruent isoscelizers point
In geometry the congruent isoscelizers point is a special point associated with a plane triangle. It is a triangle center and it is listed as X(173) in Clark Kimberling's Encyclopedia of Triangle Cent
Spieker center
In geometry, the Spieker center is a special point associated with a plane triangle. It is defined as the center of mass of the perimeter of the triangle. The Spieker center of a triangle ABC is the c
Equal detour point
The equal detour point is a triangle center with the Kimberling number X(176). It is characterized by the equal detour property, that is if you travel from any vertex of a triangle to another by takin
In triangle geometry, a Hofstadter point is a special point associated with every plane triangle. In fact there are several Hofstadter points associated with a triangle. All of them are triangle cente
Gergonne point
No description available.
Morley centers
In geometry the Morley centers are two special points associated with a plane triangle. Both of them are triangle centers. One of them called first Morley center (or simply, the Morley center ) is des
Feuerbach point
In the geometry of triangles, the incircle and nine-point circle of a triangle are internally tangent to each other at the Feuerbach point of the triangle. The Feuerbach point is a triangle center, me
De Longchamps point
In geometry, the de Longchamps point of a triangle is a triangle center named after French mathematician Gaston Albert Gohierre de Longchamps. It is the reflection of the orthocenter of the triangle a
Orthocenter
No description available.
Fermat point
In geometry, the Fermat point of a triangle, also called the Torricelli point or Fermat–Torricelli point, is a point such that the sum of the three distances from each of the three vertices of the tri
Tarry point
In geometry, the Tarry point T for a triangle ABC is a point of concurrency of the lines through the vertices of the triangle perpendicular to the corresponding sides of the triangle's first Brocard t
Centroid
In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the
Napoleon points
In geometry, Napoleon points are a pair of special points associated with a plane triangle. It is generally believed that the existence of these points was discovered by Napoleon Bonaparte, the Empero