Definition:Simson Line

Definition
Let $\triangle ABC$ be a triangle.

Let $P$ be a point on the circumcircle of $\triangle ABC$.

Construct perpendiculars from $P$ to each of the sides of $\triangle ABC$.

Let $D$, $E$ and $F$ be the feet of those perpendiculars.


 * [[File:Simson-line-1.png]]

The line $DEF$ called the Simson line.

Also known as
The Simson line is also known as Simson's line.

Also see

 * Simson Line Theorem, which proves collinearity of $D$, $E$ and $F$.