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(Solved) Re: Small circles around a bigger circle

Posted: Tue Apr 28, 2020 9:53 pm
by CVH
I found this post chain following some others post by member.
https://qcad.org/rsforum/viewtopic.php? ... =15#p23175
Doesn't it seems to be even unrelated to the topic about a drawing challenge :?: :!: :wink:

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.
The Incircle radius you asked for is R minus your smaller radius.

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... :wink:

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

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

Posted: Wed Apr 29, 2020 7:23 am
by CVH
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