Maximum Angle Explained: Circle and Tangent Construction

This GeoGebra example dynamically demonstrates how a maximum angle is formed and explained under given geometric conditions. It shows how a circle, tangents, perpendicular lines, and angle bisectors interact to make a specific angle reach its maximum value. Core mathematical concepts involve the inscribed angle theorem, tangent properties, angle bisectors, and optimization thinking. The construction uses commands such as Line, Point, OrthogonalLine, Segment, Angle, LineBisector, Midpoint, Circle, and Intersect, creating objects A, B, C, D, E, F, G, H, I, J, segments a, b, c, d, e, f, g, h, i, j, angles α and β, and intersection point T1. This is suitable for high school or early college students to grasp intuitive proofs of geometric optimization problems, and also serves as a classroom demonstration tool for teachers to link abstract theorems with dynamic visualization.