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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 ...
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.
Common nine-point circle, where N, O 4, A 4 are the nine-point center, circumcenter, and orthocenter respectively of the triangle formed from the other three orthocentric points A 1, A 2, A 3. The center of this common nine-point circle lies at the centroid of the four orthocentric points. The radius of the common nine-point circle is the ...
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.
Figure 3. A nine-point circle bisects a line segment going from the corresponding triangle's orthocenter to any point on its circumcircle. Figure 4. The center N of the nine-point circle bisects a segment from the orthocenter H to the circumcenter O (making the orthocenter a center of dilation to both circles): [6]: p.152
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 ...
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