Exploring Properties of a Circle

Start by drawing a circle with a center point and a point on the circumference to define its radius. Then choose three arbitrary points on the circle, labeling them as endpoints of chords. Construct two chords sharing one endpoint, and a third chord connecting the other two points. For each chord, draw its perpendicular bisector. Observe that all three bisectors intersect at the circle's center, demonstrating that the perpendicular bisector of any chord passes through the center. The final figure includes the circle, its center, four points on the circumference, three chords, and their perpendicular bisectors, clearly showing the geometric relationships.