Definition:Orthic Triangle

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Definition

Let $\triangle ABC$ be a triangle.

Let $\triangle DEF$ be the triangle formed by the feet of the altitudes $AD$, $BC$ and $ED$ of $\triangle ABC$.

Orthic-Triangle.png

$\triangle DEF$ is known as the orthic triangle of $\triangle ABC$.

That is, the orthic triangle of $\triangle ABC$ is the pedal triangle of its orthocenter.


Also known as

The orthic triangle of a given triangle $\triangle ABC$ is also known as the pedal triangle of $\triangle ABC$.

However, as this term is also used for the pedal triangle of any arbitrary point with respect to $\triangle ABC$, it is the policy of $\mathsf{Pr} \infty \mathsf{fWiki}$ to use the term orthic triangle consistently.


Also see

  • Results about orthic triangles can be found here.


Sources