r/R=

-1-

-2-

 

R-x=2√3*√3/2=3>x=R-3.... (1)

 x(2R-x)=2√3*2√3=12......(2) 

(R-3)(2R-R+3)=12 R^2-9=12>

R^2=21

>R=√21 tan(30)=r/√3>r=√3*1/√3=1

 r/R=(1/√21)

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