Animation 65: Dynamic Geometry of Circles and Power Functions

①This GeoGebra example demonstrates a composite dynamic geometric construction involving circles, segments, angles, and multiple transformations, where relationships between circles and power functions are visualized through slider-driven animation. ②Core mathematical concepts include circle perimeter and area, power function graphs, percentages, exponential functions, median line statistics, along with vector translation, rotation, and scaling transformations. ③Construction highlights: from the summary, commands such as Center, Intersect, Dilate, Vector, Translate, Rotate, Angle, Segment, CircleArc, and Circle are used, creating objects b, a, c, B, d, A, C, e, D, f, C', u, c', E, C'', α, g, h, k, i, j, F, p, q, r, with intersections, dilations, and rotations producing dynamically linked elements. ④Suitable for high school or early college students exploring intersections of circle geometry, functions, transformations, and statistics, and useful for educators building interactive math demonstrations.