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.

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 $F$.

Source of Name

This entry was named for Robert Simson.

Historical Note

While it is named for Robert Simson, the Simson line was in fact first introduced by William Wallace, in a paper of $1799$.