## (Solved) Re: Small circles around a bigger circle

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CVH
Premier Member
Posts: 1186
Joined: Wed Sep 27, 2017 4:17 pm

### (Solved) Re: Small circles around a bigger circle

I found this post chain following some others post by member.
Doesn't it seems to be even unrelated to the topic about a drawing challenge

Husky,
The center distance of two equal balls that touch will be the diameter itself.
What you need is a n sided regular polygon with a side length of that diameter.
With the smaller balls centers at the corners.

https://en.wikipedia.org/wiki/Regular_polygon
The circumradius R from the center of a regular polygon to one of the vertices is related to the side length s or to the apothem a by
R = s/(2sin(π/n)) = a/(cos(π/n))

Replacing s by your smaller diameter.

Andrews method is the drawing analogy of this math.
Apart from the use of CD but that detour in math will reduce to the equality of the expresions above.

The same polygon can be constructed by PG2: no Fill, no Radius, 52 Corners and poly or not.
The two references that need to be indicated would be 6.35 apart.
Just entering the side length would be easier.
Could be a nice addon for the polygon section...

PS: By drawing only correct up to 15-14 significant digits.
Real balls have a size with an endless number of significant digits.

Kind Regards,
CVH

CVH
Premier Member
Posts: 1186
Joined: Wed Sep 27, 2017 4:17 pm

### Re: (Solved) Re: Small circles around a bigger circle

So...
Another way to Rome would be.

1) CA: diam 6.35
and place where you want it. Add a second touching the first.
2) PG2: no Fill, no Radius, 52 Corners and poly or not.
and pick the two centers of the 6.35 circles.
3) LI
draw a diagonal in the polygon to obtain the center.
use one of the smaller circles center.
4) CR
draw the incircle.
5) RO
duplicate the smaller circles around.

Regards,
CVH