Circumcenter IncenterCentroid Orthocenter Created by perpendicular bisectors Created by medians Equidistant from the sides Created by angle bisectors Created by altitudes Equidistant from the vertices
The circumcenter is the center of the circumcircle of a triangle. It is equidistant from the three vertices of the triangle. It is created by the intersection of the perpendicular bisectors of the sides.
The incenter is the center of the incircle of a triangle. It is equidistant from the three sides of the triangle. It is created by the intersection of the angle bisectors of the triangle.
The centroid is the point of intersection of the medians of a triangle. It is the center of gravity of the triangle, and it divides each median into a 2:1 ratio, with the longer segment being closer to the vertex.
The orthocenter is the point of intersection of the altitudes of a triangle. It is formed by dropping perpendiculars from each vertex of the triangle to the opposite side.
It is important to note that these four points (circumcenter, incenter, centroid, and orthocenter) may or may not coincide for a given triangle. In some cases, they may all lie on the same point (in an equilateral triangle), while in other cases, they may be distinct.