Annulus

Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n.

Correct result:

n =  3

Solution:

r1=1 r2=9  r=(r2r1)/2=(91)/2=4  R=r1+r=1+4=5  a=r=4  o1=2π R=2 3.1416 531.4159  n1=o1/(2 r)=31.4159/(2 4)3.927   n=3  θ=180/n=180/3=60 ρ=r1 sinθ1sinθ=r1 sin60 1sin60 =1 sin60 1sin60 =1 0.86602510.866025=6.4641 R2=r+2 ρ=4+2 6.464116.9282 R2<R



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