C.a.R. > Applications > Difficult > Four touching circles

This construction shows a theorem about a chain of four touching circles. The touching points lie on a circle.

This follows from the fact that each quadrilateral with equal sum of opposing sides has an inscribed circle. Thinks of it the opposite way: Take four points on a circle and construct circles touching in these points!

Technical Information

In this construction, the chain of circles can be changed, such that arbitrary configurations are possible. The alternative way to present the fact would be to start with a circle and four points on it.