Properties of Tangents Drawn to Circles (Discovery Investigation)

This interactive GeoGebra example demonstrates the key properties of tangents drawn from an external point to a circle, such as equal tangent lengths and the perpendicularity between the radius and the tangent at the point of contact. The core mathematical concepts include the definition of a tangent line, the tangent length theorem, right triangle relationships, and symmetry. The construction uses GeoGebra commands: Circle to define the circle, Point to create the external point and tangent points, Distance to measure tangent segment lengths, and PointIn to assist in locating points on the circle. By dragging the external point, learners can dynamically observe how these properties remain invariant. This resource is ideal for middle or high school geometry classes, supporting discovery-based learning and teacher-led demonstrations.