Perpendicular Bisector of Chord

This GeoGebra example demonstrates the geometric property that the perpendicular bisector of any chord in a circle passes through the center of the circle. It constructs a circle, two points on the circle forming a chord, and the perpendicular bisector of that chord, visually showing the intersection points with the circle. Core mathematical concepts include chords, perpendicular bisectors, circle center and radius, and the theorem that the perpendicular bisector of a chord always passes through the center. Construction steps use GeoGebra commands: Circle to create the circle, Point to define points A and B on the circle, Segment to form the chord, LineBisector to generate the perpendicular bisector, and Intersect to find the intersection points C and D with the circle, with auxiliary objects f, g, a, b for completeness. Suitable for middle school geometry to verify circle properties, and for high school coordinate geometry to understand line-circle relationships.