Constant sum of squared distances from a circle point to a regular polygon

This example demonstrates a key geometric invariant: as a point moves on a concentric circle, the sum of the squared distances from the point to the vertices of a regular polygon remains constant. It highlights concepts such as concentric circle geometry, regular polygon vertex construction, Euclidean distance, and the use of squared-distance summation to reveal a position-independent quantity. The construction in GeoGebra is driven by parameters (r, R, n, t) to generate the polygon vertices (V_1…V_12 in a sequence) and the moving point P on the circle, compute each distance (dist) from P to every vertex, then aggregate the squared distances using Sum to form Sd2 (and related displays like Sd, TableText/Textfield, and input/display objects such as CasillaDeEntrada1). Suitable for high-school to early undergrad students studying geometric invariants, algebraic verification, and classroom exploration with dynamic geometry tools.