Monge's theorem

In geometry, Monge's theorem, named after Gaspard Monge, states that for any three circles in a plane, none of which is completely inside one of the others, the intersection points of each of the three pairs of external tangent lines are collinear.

Monge's theorem states that the three such points given by the three pairs of circles always lie in a straight line.

In the case of two of the circles being of equal size, the two external tangent lines are parallel.

In this case Monge's theorem asserts that the other two intersection points must lie on a line parallel to those two external tangents.

Further, the line connecting any two apex points must also intersect their center of similarity.

A visual representation of Monge's Theorem.The intersection of the red lines , that of the blue lines , and that of the green lines are collinear, all falling on the black line .