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The isogonal conjugate of the orthocenter is the circumcenter of the triangle. [10] The isotomic conjugate of the orthocenter is the symmedian point of the anticomplementary triangle. [11] Four points in the plane, such that one of them is the orthocenter of the triangle formed by the other three, is called an orthocentric system or ...
Orthocentric system.Any point is the orthocenter of the triangle formed by the other three. In geometry, an orthocentric system is a set of four points on a plane, one of which is the orthocenter of the triangle formed by the other three.
Symbol Name Meaning SI unit of measure alpha: alpha particle: angular acceleration: radian per second squared (rad/s 2) fine-structure constant: unitless beta: velocity in terms of the speed of light c: unitless beta particle: gamma: Lorentz factor: unitless photon: gamma ray: shear strain: radian
The orthocenter, the circumcenter, the centroid, the Exeter point, the de Longchamps point, and the center of the nine-point circle are collinear, all falling on a line called the Euler line. The de Longchamps point also has other collinearities.
If P is the orthocenter, then LMN is the orthic triangle. If P is the incenter, then LMN is the intouch triangle. If P is the circumcenter, then LMN is the medial triangle. If P is on the circumcircle of the triangle, LMN collapses to a line (the pedal line or Simson line). Special case: P is on the circumcircle.
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 figure. [further explanation needed] The same definition extends to any object in -dimensional Euclidean space. [1]
The nine-point center N is one-fourth of the way along the Euler line from the centroid G to the orthocenter H: [6]: p.153 ¯ = ¯. Let ω be the nine-point circle of the diagonal triangle of a cyclic quadrilateral. The point of intersection of the bimedians of the cyclic quadrilateral belongs to the nine-point circle.
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.