What happens to the perpendicular bisector of a chord in a circle?

The perpendicular bisector of a chord in a circle has a special relationship with the center of the circle. When a chord is drawn, its midpoint can be determined, and a line that is perpendicular to the chord at this midpoint is known as the perpendicular bisector. One of the fundamental properties of circles is that the perpendicular bisector of any chord will always pass through the center of the circle.

This is due to the fact that the perpendicular bisector divides the chord into two equal segments and, by geometric properties of circles, all points on this bisector are equidistant from the endpoints of the chord. The only point that is equidistant from both ends of the chord and all other points on that line is the center of the circle. Thus, the correct answer highlights this critical property, demonstrating the relationship between chords, their perpendicular bisectors, and the center of the circle.