# orthic triangle

If $ABC$ is a triangle and $AD,DE,CF$ are its three heights (http://planetmath.org/BaseAndHeightOfTriangle), then the triangle $DEF$ is called the orthic triangle of $ABC$.

A remarkable property of orthic triangles says that the orthocenter of $ABC$ is also the incenter of the orthic triangle $DEF$. That is, the heights of $ABC$ are the angle bisectors of $DEF$.

 Title orthic triangle Canonical name OrthicTriangle Date of creation 2013-03-22 12:11:00 Last modified on 2013-03-22 12:11:00 Owner drini (3) Last modified by drini (3) Numerical id 8 Author drini (3) Entry type Definition Classification msc 51-00 Related topic Triangle Related topic Orthocenter Related topic EulerLine Related topic CevasTheorem Related topic CyclicQuadrilateral Related topic TrigonometricVersionOfCevasTheorem Related topic BaseAndHeightOfTriangle