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  2. Centroid - Wikipedia

    en.wikipedia.org/wiki/Centroid

    A triangle's centroid is the point that maximizes the product of the directed distances of a point from the triangle's sidelines. [ 20 ] Let A B C {\displaystyle ABC} be a triangle, let G {\displaystyle G} be its centroid, and let D , E , F {\displaystyle D,E,F} be the midpoints of segments B C , C A , A B , {\displaystyle BC,CA,AB,} respectively.

  3. List of centroids - Wikipedia

    en.wikipedia.org/wiki/List_of_centroids

    The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object X {\displaystyle X} in n {\displaystyle n} - dimensional space is the intersection of all hyperplanes that divide X {\displaystyle X} into two parts of equal moment about the hyperplane.

  4. Triangle center - Wikipedia

    en.wikipedia.org/wiki/Triangle_center

    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 .

  5. Triangle - Wikipedia

    en.wikipedia.org/wiki/Triangle

    The Kiepert hyperbola is unique conic that passes through the triangle's three vertices, its centroid, and its circumcenter. [66] Of all triangles contained in a given convex polygon, one with maximal area can be found in linear time; its vertices may be chosen as three of the vertices of the given polygon. [67]

  6. Euler line - Wikipedia

    en.wikipedia.org/wiki/Euler_line

    In geometry, the Euler line, named after Leonhard Euler (/ ˈ ɔɪ l ər / OY-lər), is a line determined from any triangle that is not equilateral.It is a central line of the triangle, and it passes through several important points determined from the triangle, including the orthocenter, the circumcenter, the centroid, the Exeter point and the center of the nine-point circle of the triangle.

  7. Median (geometry) - Wikipedia

    en.wikipedia.org/wiki/Median_(geometry)

    The triangle medians and the centroid.. In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. . Every triangle has exactly three medians, one from each vertex, and they all intersect at the triangle's cent

  8. Isosceles triangle - Wikipedia

    en.wikipedia.org/wiki/Isosceles_triangle

    Isosceles triangle showing its circumcenter (blue), centroid (red), incenter (green), and symmetry axis (purple) The inradius and circumradius formulas for an isosceles triangle may be derived from their formulas for arbitrary triangles. [30]

  9. Section formula - Wikipedia

    en.wikipedia.org/wiki/Section_formula

    In coordinate geometry, the Section formula is a formula used to find the ratio in which a line segment is divided by a point internally or externally. [1] It is used to find out the centroid, incenter and excenters of a triangle. In physics, it is used to find the center of mass of systems, equilibrium points, etc. [2] [3] [4] [5]