Do All Triangles Have an Orthocenter?

It appears that all acute triangles have the orthocenter inside the triangle. Depending on the angle of the vertices, the orthocenter can “move” to different parts of the triangle.

Can the orthocenter be outside of the triangle?

The orthocenter is always outside the triangle opposite the longest leg, on the same side as the largest angle. The only time all three of these centers fall in the same spot is in the case of an equilateral triangle.

Is the centroid always inside the triangle?

* The centroid of a triangle is always inside of the triangle, and it moves along a line segment side to side. 2. The ORTHOCENTER(H) of a triangle is the common intersection of the three lines containig the altitudes. An altitude is a perpendicular segment from a vertex to the line of the opposite side.

Alexander Ross

Alexander Ross

Gaming, Esports & Interactive Media Writer

Alexander Ross has covered the video game industry for a decade, writing deep dives on game design, esports tournaments, VR developments, and gaming culture.