Distance Between Chords and the Centre of a Circle

This applet demonstrates the geometric properties relating chords to the center of a circle. It constructs a circle along with one or more chords and draws perpendicular segments from the center of the circle down to each chord. Through interactive manipulation, students can drag the chords to different positions and observe how the distance from the center to the chord, the length of the chord itself, and the fixed radius of the circle are all interconnected. The applet visually reinforces the key theorem that a perpendicular drawn from the center of a circle to a chord bisects that chord, commonly known as the perpendicular bisector theorem or垂径定理. This means that whenever a radius or line segment from the center meets a chord at a right angle, it splits the chord into two equal halves. Students can verify this relationship dynamically by moving the chords around the circle and watching the corresponding distance and chord length values update in real time. The interactive nature of the applet allows learners to explore multiple chords simultaneously, compare their distances from the center, and discover the pattern that chords equidistant from the center are equal in length, while chords closer to the center are longer and those farther away are shorter. This hands-on exploration helps solidify the fundamental circle properties taught in secondary school geometry curricula. By combining visual representation with numerical feedback, the applet bridges the gap between abstract theorem statements and concrete geometric understanding, making it an effective teaching tool for classroom instruction or independent study.