New Pythagorean Theorem for Circumferences: Quadrilateral Perimeter and Geometri

This GeoGebra example demonstrates a new Pythagorean-type theorem related to circumferences (circumcircles), exploring the squared relationships among side lengths, perimeters, and other geometric quantities of a general quadrilateral inscribed in a circle. Core mathematical concepts include generalizations of the Pythagorean theorem, circle geometry, quadrilateral properties, geometric mean, symmetry, and vectors. Construction details: using GeoGebra commands such as Circle, Point, Line, Intersect, Segment, Rotate, Angle, Midpoint, Area, PointIn, Circumference, and OrthogonalLine, the construction creates points A, B, C, D, E, F, G, H and multiple text objects, with auxiliary lines built via rotation, midpoints, and orthogonal lines, and computes areas and perimeters. Suitable for high school and above, this example is ideal for exploring theorem generalizations, dynamic verification, and mathematical proof, as well as for math experiments or inquiry-based learning.