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 triangleMathworldPlanetmath of ABC.

A remarkable property of orthic triangles says that the orthocenterMathworldPlanetmath of ABC is also the incenterMathworldPlanetmath of the orthic triangle DEF. That is, the heights of ABC are the angle bisectorsMathworldPlanetmath 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