NB.I propose this solution. The posted solutions are algebraic.
NB. amoeba is the simplex optimization method found at www.jsoftware.com
require'amoeba'['/usr/local/j64-602/addons/math/misc/amoeba.ijs'
NB. y is Cx0 Cy0 R0 Cx1 Cy1 R1 Cx2 Cy2 R2
NB. x are radius scale factors to control which circles are included
NB. in the common tangent circle. 1 to surround, _1 to exclude.
NB. returns (center, radius); final simplex volume
apollonius =: 3 :0
1 apollonius y
:
a=.9$0 0 1 NB. boolean selection vector
c=.3 2$(-.a)#,y NB. centers
r=.x*a#,y NB. radii
v=.1e_20 NB. goal simplex volume
NB. scale the problem rather than the volume?
d=:r 2 : 'm + [: +/"1&.:*: n -"1 ]' c NB. distances to tangents
s=.([: +/ [: *:@, -/~@:d) amoeba v c NB. solution
avg =. +/ % #
((, avg@:d)&.:>@:{. , {:)s
)
NB. all 8 solutions
(<:+:#:i.8)apollonius"1 _ ] _1 1 1,4 2 2,:1 _3 3
NB........graphical demonstration...........
load'graph'
p0 =: 1,.~|:2 1 o./ 2p1 * (i. % <:) 80
draw =: 4 : 0
gdclose name=:'apollo'
gdopen name
gdcolor GREEN
gdpolygon ,/"2 p0(+/ .*)("_ _1)0.1*((0 1,3 4,:6 7){,y),"2 1~(2 5
8{,y)*/=i.2
gdcolor RED
gdlines ,p0+/ .*0.1*(2{.,x),~({:,x)*=i.2
gdshow name
)
(draw~ >@{.@:((-_1 1 1)&apollonius))_1 1 1,4 2 2,:1 _3 3
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