Attachment 24535

Let say R= Radius of the big circle.

r= radius of the small circles

n= number of small circles in the big circle

What would be the formula to figure out the 'r' for n number of small circles within that R radius big circle.

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- Aug 18th 2012, 10:29 AMameerulislamRadius of equally sized small circle of a big Circle?!
Attachment 24535

Let say R= Radius of the big circle.

r= radius of the small circles

n= number of small circles in the big circle

What would be the formula to figure out the 'r' for n number of small circles within that R radius big circle. - Aug 18th 2012, 11:51 AMearbothRe: Radius of equally sized small circle of a big Circle?!
1. The midpoinst of the small circles form a regular polylateral with the side-length 2r. You have n isosceles triangles.

2. The central angle of one of the isosceles triangles is , that means must be a divisor of 360°.

3. Each isosceles triangle can be split into 2 right triangles with

4. Keep in mind that - Aug 19th 2012, 03:33 AMameerulislamRe: Radius of equally sized small circle of a big Circle?!
- Aug 19th 2012, 05:59 AMearbothRe: Radius of equally sized small circle of a big Circle?!
An example: You know (from my previous post) that

Now choose a value for which must be a divisor of 180:

To each value of belongs the number of small circles:

Of course you can choose the number of circles first and determine the value of afterwards:

For instance: You want to draw 7 small circles then

But in both cases you have to use the Sine function.