Definition:Pedal Triangle/Point

Definition

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 $PF$.

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$\triangle DEF$ is known as the pedal triangle of $P$ with respect to $\triangle ABC$.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): pedal triangle: 1. (of a point with respect to a given triangle)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): pedal triangle: 2. (of a point with respect to a triangle)