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