POLYGONS AND CIRCLES  
Section: Geometry  
1. CIRCLES AND POLYGONS (5sided)  
In the following window you can see that a regular polygon is found inside a circle that passes through all its vertices. This circle is called the circumscribed circle. There is also a circle which forms a tangent with the midpoints (M) of the sides which is called the inscribed circle. 

1. Rotate this polygon until the circumscribed and inscribed circles are drawn.

2. CIRCLES AND POLYGONS (4 and 8sided)  
In the following window you can see the circumscribed and inscribed circles of two polygons: a 4sided one and an 8sided one. 

1.
Note that the more
sides the polygon has, the closer it is in shape to the circle that
circumscribes it.
2. What are the circles like that circumscribe the square and the octagon?

3. CIRCLES AND POLYGONS (20sided)  
In the following window you can see the circumscribed and inscribed circle of a 20sided polygon. 

1. Rotate the 20sided polygon until the circumscribed and inscribed circles are drawn. 2. Don't you think the polygon looks like a circle? It almost fits perfectly between the circumscribed and inscribed circles.

Agustín Muñoz Núñez  
Spanish Ministry of Education. Year 2001  
Except where otherwise noted, this work is licensed under a Creative Common License