Question 320470
{{{drawing(300,300,-10,10,-10,10,
line(0,0,0,10),line(0,0,10,0),blue(line(0,0,-2.1,-2.1)),
circle(0,0,3),
circle(6,0,0.2),
circle(3,5.2,.2),
line(6,0,3,5.2),
line(0,0,3,5.2),
green(line(0,0,4.5,2.6)),
green(line(0,0.1,6,0.1)),
green(line(4.5,2.6,6,0.1)),
locate(-0.5,-1,R1),
locate(4.5,0,R),
locate(5.8,2.5,R)
circle(5.5,0,3),circle(3,5.2,3))}}}
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I think this is what you mean.
The inner circle has a radius, {{{R1}}}.
The outer 6 circles have a radius of {{{R}}} and occur every 60 degrees.
Only two of them are shown here. 
The green right triangle formed by the circles has a hypotenuse of,
{{{H=R1+R}}}
The green opposite leg of the triangle is {{{R}}}.
The angle opposite the green leg is {{{(1/2)(60)=30}}}.
From trigonometry,
{{{sin(30)=OPP/HYP}}}
{{{0.5=R/(R1+R)}}}
{{{R=0.5(R1+R)}}}
{{{2R=R1+R}}}
{{{R1=R}}}
You also know that,
{{{R1+R+R=3}}}
{{{R1=R=1}}} cm