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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 .
Of the nine points defining the nine-point circle, the three midpoints of line segments between the vertices and the orthocenter are reflections of the triangle's midpoints about its nine-point center. Thus, the nine-point center forms the center of a point reflection that maps the medial triangle to the Euler triangle, and vice versa. [3]
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.
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.
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]
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
At one point an officer asks for the location of a “playground” she had mentioned. “Outside the, the…outside the, um…hotel,” Monclave responded.
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.
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