Tangent Circles Family: Dynamic Construction in GeoGebra

This example demonstrates how to construct a family of mutually tangent circles using GeoGebra and explore their geometric properties. The core mathematical concepts include tangents to circles, points of tangency, relative positions of circles and lines, and generating tangent circle families via homothety (dilation). Construction highlights: from the construction summary, commands such as Circle, Point, Tangent, Line, Intersect, Segment, Polygon, Dilate, and Angle are used, involving objects like multiple circles (c, r_0, r_1, r_2), tangent points (T_0, T_1), centers (O_0, O_1, O_2), auxiliary lines, and text labels. The Dilate command generates circles of different radii that are tangent to each other, and the Angle tool marks relevant angles. Suitable for high school or early college students learning geometric construction, tangent properties, and dynamic geometry software, as well as for classroom demonstrations by teachers.