Tangent Lines To Circles - Tangent Lines To Three Circles: Monge's Theorem

Tangent Lines To Three Circles: Monge's Theorem

For three circles denoted by C₁, C₂, and C₃, there are three pairs of circles (C₁C₂, C₂C₃, and C₁C₃). Since each pair of circles has two homothetic centers, there are six homothetic centers altogether. Gaspard Monge showed in the early 19th century that these six points lie on four lines, each line having three collinear points.