Back مركز مثلث Arabic Виçкĕтеслĕхĕн чаплă пăнчисем CV Ausgezeichnete Punkte im Dreieck German Elementos notables de un triángulo Spanish مرکز مثلث Persian Kolmion merkilliset pisteet Finnish Centre du triangle French מרכז משולש HE Եռանկյան նշանավոր կետեր Armenian Titik istimewa pada segitiga ID
In geometry, a triangle center or triangle centre is a point in the triangle's plane that is in some sense in the middle of the triangle. For example, the centroid, circumcenter, incenter and orthocenter were familiar to the ancient Greeks, and can be obtained by simple constructions.
Each of these classical centers has the property that it is invariant (more precisely equivariant) under similarity transformations. In other words, for any triangle and any similarity transformation (such as a rotation, reflection, dilation, or translation), the center of the transformed triangle is the same point as the transformed center of the original triangle. This invariance is the defining property of a triangle center. It rules out other well-known points such as the Brocard points which are not invariant under reflection and so fail to qualify as triangle centers.
For an equilateral triangle, all triangle centers coincide at its centroid. However the triangle centers generally take different positions from each other on all other triangles. The definitions and properties of thousands of triangle centers have been collected in the Encyclopedia of Triangle Centers.