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 $\triangle ABC$.
$\triangle DEF$ 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
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: The pedal triangle
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): pedal triangle: 2.
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): pedal triangle
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): pedal triangle: 1.
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): pedal triangle
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): pedal triangle