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If the triangle ABC is oblique (does not contain a right-angle), the pedal triangle of the orthocenter of the original triangle is called the orthic triangle or altitude triangle. That is, the feet of the altitudes of an oblique triangle form the orthic triangle, DEF .
The three altitudes of a triangle intersect at the orthocenter, which for an acute triangle is inside the triangle. The orthocenter of a triangle, usually denoted by H, is the point where the three (possibly extended) altitudes intersect. [1] [2] The orthocenter lies inside the triangle if and only if the triangle is acute.
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.
Tangential triangle; The triangle whose vertices are the points of contacts of the excircles with the respective sides of triangle ABC; The triangle formed by the bisectors of the external angles of triangle ABC; The pedal triangle of any point P in the plane of triangle ABC (and as a special case the Orthic_triangle)
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.
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 .
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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.