orthocenter
Sign in to saveright|thumb|The three altitudes of a triangle intersect at the orthocenter, which for an Acute and obtuse triangles|acute triangle is inside the triangle.
Article
10 sectionsContents
- Formulation
- Properties
- Orthocentric system
- Relation with circles and conics
- Relation to other centers, the nine-point circle
- History
- See also
- Notes
- References
- External links
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.