Explore Cyclic Polygons: Dynamic Geometry of Inscribed Shapes

This interactive GeoGebra construction invites learners to explore cyclic polygons—polygons whose vertices all lie on a common circle. By dragging points on the circle, users observe how side lengths, interior angles, and the total perimeter change, revealing key relationships such as the constant sum of interior angles and the emergence of isosceles triangles from radii. The core mathematical concepts include circle geometry, polygon angle sums, the arithmetic mean of side lengths, and the limiting behavior as the number of sides increases toward a circle. The construction is built using Circle, Point, Polygon, and Angle commands, with objects including vertices A_1, B, C, D, E, F, G, H, and measured angles α, β, γ, δ, ε. It is ideal for middle school through undergraduate geometry courses, enabling hands-on experimentation with random vertex placement and slider-based animation to visualize how perimeter relates to the number of sides and the circle's radius. This resource supports inquiry-based learning and helps students grasp fundamental concepts of cyclic polygons and their approximation to circles.