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**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.