Orthocenter (H)

The orthocenter H is the intersection of the three altitudes of a triangle, where each altitude is a line drawn from a vertex to the opposite side, forming a right angle.

Keywords: orthocenter, altitude, perpendicular, triangle centers

Prerequisites: triangle · Difficulty: beginner

The orthocenter is the point where the three altitudes of a triangle cross each other.

What's an Altitude?

An altitude is a line that goes from a corner (vertex) of the triangle down to the opposite side, making a perfect right angle ($90°$) with that side. Think of it as the "height" of the triangle from that vertex.

Every triangle has three vertices, so it has three altitudes. They all meet at a single point, which is the orthocenter.

Fun Fact

The location of the orthocenter depends on the type of triangle:

• For an acute triangle (all angles less than $90°$), the orthocenter is inside the triangle.
• For a right triangle, the orthocenter is on the vertex with the right angle.
• For an obtuse triangle (one angle greater than $90°$), the orthocenter is outside the triangle!