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 $DEF$.