[tex]a)~ r= \frac{l_{\Delta} \sqrt{3}}{6} \Rightarrow l_{\Delta} = \frac{6r}{ \sqrt{3} }= \frac{6 \sqrt{3}r }{3}=2 \sqrt{3}r. \\ A_{\Delta}= \frac{ l_{\Delta} ^{2} \sqrt{3} }{4 }= \frac{4*3* r^{2} \sqrt{3} }{4}= 3r^{2} \sqrt{3}. \\ l_{\boxed{}}=r \sqrt{2}. \\ A _{\boxed{}}= l_{\boxed{}} ^{2} =2 r^{2} . \\ \frac{ A_{\Delta} }{ A_{\boxed{}} }= \frac{3 r^{2} \sqrt{3} }{2 r^{2} } = \frac{3 \sqrt{3} }{2}=constant. [/tex]
[tex]b)~ l_{1}-latura~patratului~circumscris~cercului \\ l_{2} -latura~patratului~inscris~in~cerc \\ \\ l_{1} =2R \\ A_{1}= (l_{1})^2=4R^{2} \\ l_{2}=R \sqrt{2} \\ A_{2} = (l_{2})^{2} = 2R^{2} \\ \\ \frac{A_{1}}{A_{2}} = \frac{4R^2}{2R^2}=2=constant. [/tex]
