Constant Distance from an Interior Point to the Radical Axis

This GeoGebra applet demonstrates the geometric properties arising from the power of a point theorem and the radical axis. A fixed circle A serves as the base circle. A point C moves along the circumference of circle A, while a fixed interior point D is placed inside circle A. A moving circle is constructed with its center at C and radius equal to the segment CD. For every position of C on the fixed circle, the radical axis of the two circles is constructed. The construction then draws the perpendicular from the fixed interior point D to this radical axis, with the foot of the perpendicular labeled as G. The applet visually reveals that the distance DG from the fixed interior point D to the radical axis remains constant throughout the motion of point C. This invariant distance property elegantly connects classical Euclidean geometry with analytic concepts. Students can drag point C around the fixed circle and observe in real time how the moving circle changes while its radical axis with the fixed circle shifts accordingly, yet the perpendicular distance from D to the radical axis never varies. The interactive nature of the model makes it an effective teaching tool for deepening understanding of the radical axis, circle power, and locus problems. It is particularly suited for advanced study in plane geometry and analytic geometry, providing an intuitive visual foundation before transitioning to formal algebraic proofs.