Exploring the Relationship Between Chords and the Centre of a Circle

This GeoGebra applet demonstrates the geometric relationship between chords and the center of a circle. By constructing a circle, chords, and the line segment from the center to the midpoint of a chord, it visually illustrates the connections between the distance from the center to the chord, the chord length, and the subtended central angle. Using dynamic interaction, users can drag points to alter the position and length of the chord in real time, observing how the distance from the center to the chord changes accordingly. The applet helps learners explore two key theorems: first, that the perpendicular from the center of a circle to a chord bisects the chord; and second, that equal chords are equidistant from the center of the circle. Students can measure and compare chord lengths, central angles, and distances simultaneously, reinforcing the intimate link between these three quantities. When a chord moves closer to the center, its length increases and the subtended central angle widens; when it moves farther away, both decrease. This dynamic visualization makes abstract geometric relationships tangible and intuitive. The interface is designed for easy manipulation, allowing students to experiment freely without any prior expertise in GeoGebra. Teachers can use this tool in classroom settings as a supplementary demonstration or assign it as an independent exploration activity. It is particularly well suited for middle school and high school geometry courses covering circles and their properties. By actively engaging with the construction, students develop deeper conceptual understanding rather than relying solely on memorization of theorems. The applet also supports formative assessment, as instructors can pose guided questions such as asking students to predict how the chord length will change when the distance from the center is modified, then verify their predictions through dragging and measuring. Overall, this interactive applet serves as a powerful visual aid for mastering fundamental circle geometry and building a strong foundation for more advanced topics in Euclidean geometry.