Search results
Results from the WOW.Com Content Network
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 .
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. For a right triangle, the orthocenter coincides with the vertex at the right angle. [2]
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.
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 midpoint of the line segment from each vertex of the triangle to the orthocenter (where the three altitudes meet; these line segments lie on their respective altitudes). In 1822, Karl Feuerbach discovered that any triangle's nine-point circle is externally tangent to that triangle's three excircles and internally tangent to its incircle ...
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 ...
orthocenter: intersection of the three altitudes: X(5) nine-point center: center of the nine-point circle: X(6) symmedian point: intersection of the three symmedians: X(7) Gergonne point: symmedian point of contact triangle X(8) Nagel point: intersection of lines from each vertex to the corresponding semiperimeter point X(9) Mittenpunkt
Consider three pairwise distinct vectors of equal length , and each of them acting on the same point thus creating the points , and .Those points form the triangle with as the center of its circumcircle.