[tex] \frac{ A_{T} }{ A_{L} } = \frac{ \pi R(R+G)}{ \pi RG}= \frac{R+G}{G} \\ [/tex]
Utilizind teorema cosinusului in triunghiul cu laturile G;G si 2R
[tex]4R^2=G^2+G^2-2*G*G*cos120 \\ 4R^2=2G^2+G^2 \\ 4R^2=3G^2 \\ R= \frac{G \sqrt{3} }{2} [/tex]
Substituim mai sus obtinem
[tex] \frac{ A_{T} }{ A_{L} }= \frac{ \frac{G \sqrt{3} }{2}+G }{G}= \frac{G( \sqrt{3}+2) }{2G}= \frac{ \sqrt{3}+2 }{2} [/tex]
