Simson Lines

Given a $\bigtriangleup ABC$ and a point $P$ on its circumcircle. The line segments from $P$ perpendicular to sides $AB$, $AC$, and $BC$ are named $D$, $E$, and $F$ respectively. These three points are collinear

And the line that passes through $D$, $E$, and $F$ is called the____of $\bigtriangleup ABC$

The converse is also true.

The Simson line can also be generalised to angles not equal to 90 degrees. The general statement is as follows:

Given a point $P$ on the circle $(ABC)$, points $Q, R, S$ lie on AB,BC and CA respectively such that $\angle PQB= \angle PRB= \angle PSC$ then Q, R, S are collinear. The converse is also true.