orthocenter

right|thumb|The three altitudes of a triangle intersect at the orthocenter, which for an Acute and obtuse triangles|acute triangle is inside the triangle.

The orthocenter of a triangle, usually denoted by , is the point where the three (possibly extended) altitudes intersect. The orthocenter lies inside the triangle if and only if the triangle is acute. For a right triangle, the orthocenter coincides with the vertex at the right angle. For an equilateral triangle, all triangle centers (including the orthocenter) coincide at its centroid.