### Author Topic: Circles in Circle 1  (Read 5499 times)

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#### Visio Guy

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##### Circles in Circle 1
« on: November 18, 2014, 08:22:31 AM »
Align circles around the inner edge of a larger circle...without ShapeSheet or code!

Circles in Circle 1
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#### kharkaltar

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##### Re: Circles in Circle 1
« Reply #1 on: November 20, 2014, 01:20:49 PM »
Hello,

You can also use math to find the radius of the smalls circles.
g = angle = 360/Number-of-circles

r = R*SQRT((1 -cos(g))² + sin(g)²) / (2 + SQRT( (1 – cos (g))² + sin(g)²))

See attached VSD file.

First page is the math formula described
second page is an example of an automated set of circles.

regards,
Jerome.

#### vojo

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##### Re: Circles in Circle 1
« Reply #2 on: November 20, 2014, 02:45:00 PM »
cool

smells like a macro to create on the fly

maybe even all shapesheet for up to say 10 circles (hide unused based on small circle count).

But cool

Curiously, where did you find info on the math involved?

#### Visio Guy

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##### Re: Circles in Circle 1
« Reply #3 on: November 21, 2014, 05:13:23 AM »
You guys are reading my mind!

When I worked out the small-circle radius a few days ago, I wound up with something simpler:

r = RSinA2/(1 + SinA2)

A2 is 1/2 of "A1". A1 is 360deg/Ct, which is kharkaltar's "g"

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#### wapperdude

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##### Re: Circles in Circle 1
« Reply #4 on: November 21, 2014, 11:22:00 AM »
Yep!  Both formulas give same value.  Both blow up for count = 1.  OK.  That's a degenerate case!

Note.  Most literature gives the radius of larger circle in terms of unit radius of smaller circle.  Well, technically, diameters, but the formula is unchanged.
Attached Excel file computes both formulas.  Allows user to enter a value for the small circle radius.

Wapperdude
« Last Edit: November 21, 2014, 11:33:36 AM by wapperdude »
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