Geometric Construction for Iccarah Theorem: Circles, Ellipse, and Area

This example demonstrates an Iccarah-theorem related configuration by interactively constructing key points, lines, and segments, using symmetry (mirror) to reveal consistent geometric relationships among circle and ellipse elements. The core ideas include inscribed/circumscribed circle concepts (incircle/circumcircle), symmetric correspondence generated by reflection, and the use of ellipse geometry to connect visual structure with measurable quantities. In the construction, GeoGebra commands such as Point, Line, and Intersect create the basic framework and intersection points; Segment defines measurable boundaries; Mirror generates reflected (corresponding) objects; Ellipse and Circumference specify the relevant conic/circular loci. Area is used to compute region measures, while PointIn helps determine whether points lie in the constructed sets. The example also visualizes computed results and labels them with Text, and it includes objects representing differences of major geometric quantities (e.g., differenceof2major), supporting a “construct → measure → verify” learning workflow. Suitable for advanced secondary geometry, contest preparation, and introductory university geometry/analytic geometry visualization.