Wuhan No.2 High School 2018 Math Q23(2): Equilateral Triangle and Locus

This interactive GeoGebra applet provides a comprehensive, dynamic visualization of the geometric construction and solution process for Question 23, Part 2, from the 2018 Wuhan No.2 High School specialized admission mathematics examination. The problem centers on advanced Euclidean geometry, specifically focusing on the intricate properties of equilateral triangles, line segments, and the rigorous determination of point loci. It challenges students to navigate complex spatial relationships and apply transformational geometry to find the trajectory of a moving point under strict geometric constraints. Through its dynamic interface, the applet meticulously breaks down the problem-solving process step by step. Users can observe the strategic construction of auxiliary lines, the identification of critical intersection points, and the application of geometric transformations such as dilations. Furthermore, it showcases the precise construction of circles that are essential to defining the boundaries and paths of the moving points. A standout feature of this demonstration is its ability to plot and animate the locus of specific points as underlying geometric parameters change. By interacting with the applet, dragging base points, or adjusting sliders, students can watch the trajectory trace out in real time. This transforms an abstract geometric proof into a vivid, observable path, clearly illustrating how the locus behaves as the equilateral triangle and associated segments shift. For students preparing for rigorous high school entrance exams or mathematics competitions, this applet serves as an invaluable learning tool. It bridges the gap between static textbook diagrams and dynamic spatial reasoning. By visually deconstructing the auxiliary line strategies and transformational steps, learners can develop a deeper intuition for tackling complex locus problems. It not only clarifies the specific solution to this challenging exam question but also equips students with versatile problem-solving heuristics. Ultimately, it empowers learners to confidently explore positional relationships, master the art of geometric construction, and understand locus variations in complex geometric figures.