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'Polycircles' printed from

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tri-circle quad-circle pent-circle




Generalise still more! What about 4 circles? 5 circles? $n$ circles?

Experiment with the interactivities below or do the construction for yourself with ruler and compasses or using dyanamic geometry software.

The next applet is a 5-sided polygon. Again you can check that wherever you move the vertices off the polygon, the circles centred at those points will remain tangent to their two adjacant circles. Can you calculate the radii given the lengths of the sides of the polygon?

In the final applet below we have a quadrilateral. Here you see that there are 4-sided polygons where the 4 circles are not all tangent to one another. Can you make the red and green circles lie on top of one another? Then you have made all the circles tangent to their neighbours.

Created with GeoGebra

For the final challenge, what is the locus of the centre of the red and green circles when it moves so that these circles are coincident, always touching their neighbours, maintaining a perfect polycircle?

To investigate this problem further, download a copy of GeoGebra and experiment for yourself. Geogebra is free educational mathematics software that is very easy to use and combines dynamic geometry, coordinate geometry, algebra and calculus. You can also download the Quickstart guide for beginners.