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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,597

**What is the ratio of the areas of the circle circumscribing a square and the circle which is inscribed in the square?**

Let's do it using geogebra!

1)Place 2 points at (0,0) and (6,0), they will be labeled A and B.

2) Use the regular polygon tool using A and B to create a 6 x 6 square ABCD.

3) Use the midpoint tool and get the midpoints of AD, DC and CB. Those points will be labeled E,F and G.

4)Use the Circle from 3 points tool to create an inscribed circle from point E,F and G.

5) Use the Circle from 3 points tool to create a circumscribed circle from points A,D and C.

6)Use the area tool to get the area of the inscribed circle. It will be called areae in the algebra panel.

7)Use the area tool to get the area of the circumscribed circle. It will be called areaf in the algebra panel.

8)In the input bar put g = areaf / areae and press enter.

9) Now pull B around while watching g. What do you notice about the relationship of the areas of the two circles? Strong argument for 2:1 don't you think.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**Maiya****Member**- Registered: 2011-08-11
- Posts: 124

Hello bobbym;

now,

whats geogebra..

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,597

Hi Maiya;

An interactive geometry program. With it you can do the geometry constructions they teach in school and a lot more.

Here is an introductory video:

http://www.youtube.com/watch?v=rZnKMwicW_M

Here is the homepage:

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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