Geometric Construction for Wuhan No.2 High School 2020 Exam

This GeoGebra applet provides a dynamic demonstration of the geometric construction and solution process for Question 23, Part (3) of the 2020 Wuhan No.2 High School Admission Exam. This problem is a comprehensive geometry question that integrates multiple core mathematical concepts including circles, squares, angle bisectors, and rotational transformations. The applet leverages GeoGebra commands such as intersection, rotation, line segments, and angle bisectors to visually construct the auxiliary lines required to solve the problem. As students manipulate the interactive elements, they can observe in real time how the geometric figures transform, how angles relate to one another, and how the underlying properties of circles and squares come into play throughout the proof. The dynamic visualization makes it possible to trace the logical reasoning step by step, showing exactly how each auxiliary line is introduced and why it is necessary. The problem itself tests the student ability to synthesize knowledge across different areas of Euclidean geometry. It requires recognizing when to apply a rotational transformation, understanding the properties of angle bisectors within a circular context, and using the symmetries inherent in a square to simplify the problem. The applet guides learners through each of these steps interactively, allowing them to explore different configurations and verify their understanding at every stage. This tool is particularly beneficial for students preparing for competitive middle school mathematics exams in China, where such comprehensive geometry problems are common. By making the abstract reasoning process visible and interactive, the applet helps students develop both the procedural skill of constructing auxiliary lines and the deeper conceptual understanding of why those constructions work. Educators can use it in classroom instruction or assign it for independent study, giving students a powerful visual aid that complements traditional textbook proofs and lecture-based instruction.