Search results
Results from the WOW.Com Content Network
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 ...
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.
The orthocenter (blue point), the center of the nine-point circle (red), the centroid (orange), and the circumcenter (green) all lie on a single line, known as Euler's line (red line). The center of the nine-point circle lies at the midpoint between the orthocenter and the circumcenter, and the distance between the centroid and the circumcenter ...
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.
However, while the orthocenter and the circumcenter are in an acute triangle's interior, they are exterior to an obtuse triangle. The orthocenter is the intersection point of the triangle's three altitudes, each of which perpendicularly connects a side to the opposite vertex. In the case of an acute triangle, all three of these segments lie ...
where A, B, C denote both the triangle's vertices and the angle measures at those vertices; H is the orthocenter (the intersection of the triangle's altitudes); D, E, F are the feet of the altitudes from vertices A, B, C respectively; R is the triangle's circumradius (the radius of its circumscribed circle); and a, b, c are the lengths of the triangle's sides opposite vertices A, B, C ...
This file contains additional information, probably added from the digital camera or scanner used to create or digitize it. If the file has been modified from its original state, some details may not fully reflect the modified file.
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.