Definition:Pedal Triangle
Definition
Pedal Triangle of Point with respect to Triangle
Let $\triangle ABC$ be a triangle.
Let $P$ be a point in the plane of $\triangle ABC$.
Let $PD$, $PE$ and $PF$ be perpendiculars dropped from $P$ to $BC$, $AC$ and $AB$ respectively.
Let $\triangle DEF$ be the triangle formed by the feet of the perpendiculars $PD$, $PE$ and $PF$.
$\triangle DEF$ is known as the pedal triangle of $P$ with respect to $\triangle ABC$.
Orthic (Pedal) Triangle
Let $\triangle ABC$ be a triangle.
Let $\triangle DEF$ be the triangle formed by the feet of the altitudes $AD$, $BC$ and $ED$ of $\triangle ABC$.
$\triangle DEF$ is known as the orthic triangle of $\triangle ABC$.
That is, the orthic triangle of $\triangle ABC$ is the pedal triangle of its orthocenter.
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 pedal triangles can be found here.
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): pedal triangle