orthocenter
the point of concurrency of the altitudes of a triangle
The orthocenter is a key point in a triangle that is defined as the point where the three altitudes of the triangle intersect. An altitude is a line segment drawn from a vertex of the triangle perpendicular to the opposite side.
The orthocenter is not always located inside the triangle. It can also be located outside the triangle if the triangle is obtuse. In this case, the orthocenter is located where the extended altitudes intersect.
The orthocenter has several important properties. For example, the circumcenter (the point where the perpendicular bisectors of the sides of a triangle intersect) and the orthocenter are known to be symmetric with respect to the midpoint of the side opposite to the vertex of the triangle.
Another property of the orthocenter is that it lies on the Euler line, which is a line that passes through the circumcenter, orthocenter, and centroid of the triangle. The Euler line is a special line that is associated with each triangle, and it has many interesting properties.
In summary, the orthocenter is a key point in a triangle that has important geometric and mathematical properties. It can be used to solve problems related to the geometry of triangles, and it is a fascinating topic to explore in mathematics.
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