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orthic triangle (Definition)

If $ABC$ is a triangle and $AD, DE, CF$ are its three heights, 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 $DEF$.

\includegraphics{ortho}



"orthic triangle" is owned by drini. [ owner history (1) ]
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See Also: triangle, orthocenter, Euler line, Ceva's theorem, cyclic quadrilateral, trigonometric version of Ceva's theorem
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Cross-references: angle bisectors, incenter, orthocenter, property, heights, triangle
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This is version 3 of orthic triangle, born on 2002-01-08, modified 2004-02-17.
Object id is 1447, canonical name is OrthicTriangle.
Accessed 4504 times total.

Classification:
AMS MSC: 51-00 (Geometry :: General reference works )
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