Locus: Maintaining Fixed Distance from a Point

This example demonstrates the path traced by a moving point that keeps a constant distance from a fixed point, resulting in a circle. The core mathematical concept is the definition of a circle as the set of all points at a given distance from a fixed point, which is fundamental to the idea of a locus. Construction details: using GeoGebra commands such as Segment and If, with objects including points A, P, B, segment a, and text objects text1 and text2, allowing dynamic exploration by dragging point P or using a slider. Suitable for middle school geometry to visualize the definition of a circle and the concept of locus, and for high school analytic geometry when introducing the equation of a circle.