Three Circles Tangents: Collinear Intersection Points

This GeoGebra example demonstrates a classical geometric phenomenon: for three circles, the three intersection points of the tangents drawn to each pair of circles are collinear. The core mathematical concepts involve tangent lines to circles, collinearity of points, and the Monge's theorem (a special case where the three circles are non-concentric). The construction uses GeoGebra commands: Circle to define three circles, Tangent to draw common tangents for each pair, Intersect to find the tangent intersection points, and Line to connect these points and verify their collinearity. The objects involved include A, B, c, C, D, d, E, F, e, a, b, f, g, h, i, j, k, l, m, n, p, G, H, I, q, reflecting a complete geometric construction. This is suitable for high school or college geometry courses to explore tangent properties, collinearity theorems, and dynamic geometry verification. By dragging the circles, students can observe that the three intersection points always remain on a straight line, reinforcing the concept of geometric invariants.