Three Equal Lines: Circumcircle and Function-Based Geometric Construction

This GeoGebra example demonstrates the construction of three line segments of equal length, visually linked to a circumscribed circle, step functions, and the normal distribution. The core mathematical concepts include the geometric constraint of equal-length segments, properties of circumcircles, and the overlay of function graphs (such as step functions and normal distribution) with geometric objects. The construction uses the Ray and Point commands to create key points M, B, C₁, D, A, and C, while functions f and g control the positions of segment endpoints, resulting in three equal-length lines. This example is suitable for middle and high school mathematics teachers for classroom demonstrations, helping students intuitively understand the construction of equal-length segments in dynamic geometry, and can be extended to explore interdisciplinary connections between geometry and functions. It also serves as a self-guided exploration for students interested in geometric-function hybrids.