Where is the orthocenter located in a triangle?

The orthocenter of a triangle is defined as the point where the three altitudes of the triangle intersect. An altitude is a line segment drawn from a vertex to the opposite side, forming a right angle with that side.

For different types of triangles, the location of the orthocenter varies. In an acute triangle, the orthocenter lies inside the triangle; in a right triangle, it is located at the vertex of the right angle; and in an obtuse triangle, it is found outside the triangle. Therefore, while the orthocenter's position changes with the type of triangle, its fundamental property is that it is generated from the intersection of all three altitudes.

Since the altitudes are always defined within the triangle and can extend outside or meet inside depending on the triangle's nature, knowing the definition and location characteristics is key to understanding the orthocenter's role in geometry. This makes the concept of altitudes and their point of intersection essential in determining the orthocenter.