# Calculate center coordinates of circles surrounding a larger circle

I want to draw, say, 8 smaller circles that are adjacent to the big circle the edge of a big circle, similar to this picture.

I know the center coordinates of the bigger circle $$(A, B)$$, its radius $$(R)$$,radius of the smaller circles $$(r)$$, and the number of circles I want to draw $$(n)$$.

My question is very similar to the one discussed there, with one exception. I want a formula that calculates center coordinates of circles adjacent, not those on the edge of a bigger circle. Mathematics is not my strongest side (to say the least), so I'd greatly appreciate any help. Thank you!

• I think $n$ determines $r$, so for example if you want $6$ externally tangent circles then $r$ is fixed at $r=R$ (all $7$ circles are the same size in that special case). In general, you could write $r$ as a function of $n$ and it would be strictly decreasing. Jan 14, 2019 at 20:13
• I mention that because you cannot presuppose $n$ and $r$ - most pairs that you choose will lead to impossible situations. Just presuppose $n$ and $R$ and those will together determine $r$. Jan 14, 2019 at 20:14
• Thank you, that makes sense (in lay terminology, only certain amount of circles of size will fit, correct?) Jan 14, 2019 at 20:16
• Connect the centers of the $n$ externally tangent circles and you will have a regular $n$-gon Jan 14, 2019 at 20:16
• If you choose the number of small circles and the size of the big circle, the size of the small circles is fixed, invariable, set, locked. Jan 14, 2019 at 20:17

For the 'adjacent' circles use : $$\delta = 360/n$$ where $$n$$ is the number of circles you want. Then the centers are $$c_i = ((R+r)\cos i\delta + \phi, (R+r)\sin i\delta + \phi)$$, where $$i=0,1,...,n-1$$ and $$\phi$$ is some offset rotation. Note that the small circles will not necessarily touch, but they will touch the large circle.
• I just edited it, realized I had already divided by $n$, so check the corrected version. @AntonLeontyev Jan 14, 2019 at 20:25