Tangent to a Circle: Construction and Verification (Exercise 2.8)

This example demonstrates how to construct a tangent line to a circle under a given geometric setup, and how to visually verify the tangency relationship using intersection-based construction. It centers on the key geometry idea of a circle–line tangent: the special constraint at the touch point and how candidate lines become the correct tangent when the construction conditions are met. The construction uses GeoGebra commands such as Circle to create the given circle, Segment to build required connecting pieces, Line to draw the candidate (tangent) line, and Intersect to compute crucial intersection points (including the touch point and other determining points). Objects referenced in the build (e.g., A, O, c, a, d, e, B, C, b, M, f, D, g) represent the circle, center, endpoints, auxiliary points, and the intersection-derived points used to confirm the tangency condition. Suitable for secondary school geometry practice and enrichment, especially for learners studying circle tangents and for teaching GeoGebra geometric constructions.