The perpendicular bisector of a line segment is the locus of all points that are equidistant from its endpoints. This theorem can be applied to determine the center of a given circle with straightedge and compass. Pick three points A, B and C on the circle. Since the center is equidistant from all of them, it lies on the bisector of segment A B and also on the bisector of segment B C, i.e., it is the intersection point of the two bisectors. This construction is shown on a window pane by tutor Justin McLeod (Mel Gibson) to his pupil Chuck Norstadt (Nick Stahl) in the 1993 film The Man Without a Face.

perpendicular bisector | perpendicular foot