Dynamic Proof of the Law of Sines for Obtuse Triangles

This GeoGebra example provides a dynamic, interactive proof of the Law of Sines for obtuse-angled triangles. It demonstrates that in any triangle, including those containing an obtuse angle, the ratio of a side length to the sine of its opposite angle is constant and equals the diameter of the circumscribed circle. Core mathematical concepts include the Law of Sines, obtuse triangles, circumcircle, inscribed angle theorem, and triangle interior angle relationships. The construction uses GeoGebra commands such as Circle to draw the circumcircle, Point to define vertices O, B, A, C, Polygon to form the triangle, Angle to label α, β, γ, Line and Intersect to construct auxiliary lines and intersection points D, E, F, If for conditional display of cases, and Rotate to generate transformed points B′, E′, C′ and related polygons. It is suitable for high school trigonometry instruction, classroom demonstrations, and student-led exploration of trigonometric identities in non-acute triangles.