Tangent and Curvature of a Circle

This GeoGebra example illustrates the tangent line and curvature of a circle through an interactive construction. It demonstrates that at any point on a circle, the tangent is perpendicular to the radius, and the curvature is constant, equal to the reciprocal of the radius. The construction uses commands like Intersect, Circle, Translate, and Vector to create the circle, tangent line, normal line, and translated auxiliary points, helping visualize the relationship between the tangent, normal, and curvature. It is ideal for high school or undergraduate students studying coordinate geometry, calculus, or differential geometry, and serves as a clear visual aid for teachers explaining these fundamental concepts.