In geometry, the orthocenter of a triangle is the point where the altitudes of the triangle intersect. The altitude of a triangle is a line segment that is perpendicular to a side of the triangle and passes through the opposite vertex. The orthocenter is an important point in a triangle because it can be used to find the circumcenter, the incenter, and the centroid of the triangle.
The orthocenter of a triangle is not always inside the triangle. In fact, it is only inside the triangle if the triangle is acute. If the triangle is right or obtuse, the orthocenter will be outside the triangle. However, the orthocenter is always on the Euler line of the triangle, which is the line that passes through the centroid, the circumcenter, and the incenter of the triangle.
