Chords Equidistant from the Center

This GeoGebra applet demonstrates a fundamental theorem in plane geometry: in the same circle or in equal circles, chords that are equidistant from the center are equal in length, and conversely, equal chords are equidistant from the center. The applet dynamically constructs a circle along with its chords, perpendicular segments from the center to each chord, and the midpoints of those chords. Users can drag and manipulate the positions of the chords to observe in real time how the distance from the center (the chord distance) changes as the chord length varies, reinforcing the bidirectional relationship between these two quantities. The construction also illustrates how the perpendicular from the center of a circle to a chord bisects the chord, which is a key geometric property used in the proof. By connecting the radius, the chord distance, and half the chord length into a right triangle, the applet helps students visualize and understand how the Pythagorean theorem underpins the proof of this theorem. This interactive approach transforms an abstract geometric result into an intuitive visual experience. The applet is designed for middle school and high school geometry instruction, supporting both classroom demonstration and independent student exploration. It is particularly useful for helping learners grasp not only the statement of the theorem but also the logical steps involved in its proof, while developing spatial reasoning and geometric intuition through hands-on interaction.