If the outer circles are all equal radius r, and spaced at equal radius from center C, then the points at the centers of the smaller circles will form a regular n-gon (where n == the number of smaller circles).
Designate two of those adjacent centers C1 and C2. Designate the center of your big circle C0.
The angle C1-C0-C2 will be 360/n. Call that angle A.
Draw a line from C1 to C2, and its midpoint will be where your smaller circles are tangent. Designate that point P.
Now you have a triangle C0-C1-P. The angle P-C0-P1 will be A/2, and C0-P-C1 will be a right angle.
You know that the length of the segment C1-P = r.
Designate the segment C0-P as X.
Tan(A/2) = r/X, therefore:
X=r/Tan(A/2).
Therefore the length of the segment
C0-P = r / (tan((360/n)/2)
= r / (tan (180/n))
For example:
Four circles of r = 1: n=4, r=1.
X= 1/(tan(180/4)
X=1/(tan(45));
X= 1/1
X=1
Five circles of radius 2: n=5, r=2
X=2/tan(180/5)
X=2/tan(36)
X=2.7528
