## Four circles

 A special type of the circle-type is the structure consisting of four circles. It is a double element configuration where one of the elements is the circle in infinity. Therefore the inverse radiuses of the four circles is part of the arithmetical configuration. In addition comes the relations between the four circles. When all the relations are general, the arithmetical expression is large. When special circumstances occur, such at tangency of the circles, or they are orthogonal to each other, then the expression is simplified. One could in some sense characterize the species that occur as being more stable than the general. For our mind it is so. When tangency appears, then we have something to hold on to,something is settled. The same true when circles becomes orthogonal to each other; we see that something comes to rest. From this point of view, the general formulas is something that yields as something living that has not come to rest. When it does so, the different species arise. The four-circle configuration comes from the more general ten-circle structure. And this can also develop to many special situations. We shall start to consider the structure where one of the four circles change into a line, and where the other circles are tangent or orthogonal to this, and tangent or orthogonal to each other. There are in all 16 such configuration, and in all of these configurations there is a formula connecting the radiuses of the three circles.

### Four circles examples

 Construction: Ortho Circle Descartes theorem Orto Tang Orto Tang2 Orto Tang3 Apollonius Line-ortho Line-ortho   The orthocircle
 Calculation area Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Continuity