Orthocenter of A Triangle

Defined with examples and pictures

Definition of the Orthocenter of a Triangle

The orthocenter is one of the triangle's points of concurrency formed by the intersection of the triangle's 3 altitudes.

These three altitudes are always concurrent. In other, the three altitudes all must intersect at a single point , and we call this point the orthocenter of the triangle.

If the triangle is obtuse, such as the one on pictured below on the left, then the orthocenter will be exterior to the triangle.

If the triangle is acute, then the orthocenter is located in the triangle's interior

Picture of Orthocenter of a Triangle

What about the orthocenter of a right triangle?

The illustration above demonstrates that the orthocenter of an obtuse triangle is situated in the triangle's exterior; while an acute triangle's orthocenter is located in the interior. So the question is, where is the orthocenter located in a right triangle?

The orthocenter is actually concurrent with the right angle! In other words, the orthocenter is located where the right angle's vertex is (see red point in the pic below)

Picture of orthocenter of right triangle
to Triangle Points of Concurrency to Orthocenter Applet