The three corners of any triangle ABC define a circle that surrounds it, called its circumcircle. And for any point *P* on this circle, the three points closest to P on lines AB, AC, and BC are collinear.

The converse is also true: Given a point *P* and three lines no two of which are parallel, if the closest points to *P* on each of the lines are collinear, then *P* lies on the circumcircle of the triangle formed by the lines.

This discovery is named for Robert Simson, though, as often happens, it was first published by someone else — William Wallace in 1797.