Geometric Proof of the Law of Sines via Circumcircle Construction

This example demonstrates a geometric proof of the Law of Sines by constructing a circumcircle for a triangle and using angle relationships inside that circle. The central mathematics includes the link between triangle angles and their opposite sides, the circumradius, and theorems about inscribed angles versus central angles, together with the way sine values correspond to chord/arc geometry on a fixed circle. The construction follows the key GeoGebra commands listed in the source: Circle to create the circumcircle, Center to locate the circle’s center, Midpoint for auxiliary points, Segment to draw the relevant sides/chords, and Angle to measure and label angles (e.g., α, β, γ and related angles such as θ). Objects such as points A, B, C, the circumradius R, and side-length labels (a, b, c) are used to structure the proof. Suitable for high school geometry/trigonometry and early undergraduate geometry courses, especially for interactive classroom explanation and visual reinforcement of the Law of Sines.