A perpendicular bisector of a chord passes through the _____ of the circle.

The perpendicular bisector of a chord in a circle has a unique geometric property: it always passes through the center of the circle. This relationship is rooted in the symmetry of circles and the definitions of chords, segments, and bisectors.

When a chord is defined within a circle, it connects two points on the circumference. The perpendicular bisector of this chord is a line that not only divides the chord into two equal segments but also intersects it at a right angle. Due to the circle's symmetrical nature, this bisector aligns with the radius that also extends from the center of the circle to the midpoint of the chord.

Consequently, any perpendicular drawn from the center of the circle to the chord will bisect the chord at a right angle. This principle underlines that for any given chord, its perpendicular bisector will invariably pass through the circle's center. Understanding this key relationship is crucial for tasks involving chord properties and circle geometry.