Five circles

On the line segment CD = 6 there are 5 circles with radius one at regular intervals. Find the lengths of the lines AD, AF, AG, BD, and CE

Correct result:

d =  4.5826
f =  2.1794
g =  3.1225
b =  3.6056
c =  2.6458

Solution:

r=1 h=v(A,CD) AS1 S2=Δ111,α=β=γ=60, h=3/2 r=3/2 10.866  x1=(4+1/2) r=(4+1/2) 1=92=4.5 d=AD d=x12+h2=4.52+0.8662=21=4.5826
f=AE  x2=4/2 r=4/2 1=2  f=x22+h2=22+0.8662=2.1794
g=AG x3=6/2 r=6/2 1=3 g=x32+h2=32+0.8662=3.1225
b=BD x4=7/2 r=7/2 1=72=3.5 b=x42+h2=3.52+0.8662=13=3.6056
c=CE x5=5/2 r=5/2 1=52=2.5 c=x52+h2=2.52+0.8662=7=2.6458



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