[tex]\text{Notam laturile cu a,b si c.Avem ca:}\\
(a,b,c)d.p.(\sqrt5-\sqrt3,\sqrt5+\sqrt3,4)\Rightarrow \dfrac{a}{\sqrt5-\sqrt3}=\dfrac{b}{\sqrt5+\sqrt3}=\dfrac{c}{4}=k\Rightarrow\\
a=(\sqrt5-\sqrt3)k,b=(\sqrt5+\sqrt3)k,c=4k\\
\text{Afla m aria cu formula lui Heron:}\\
\boxed{A=\sqrt{p(p-a)(p-b)(p-c)}},\text{unde p este semiperimetrul}\\
p=\dfrac{a+b+c}{2}=\dfrac{(\sqrt5-\sqrt3)k+(\sqrt5+\sqrt3)k+4k}{2}=(2+\sqrt5)k\\
\text{Atunci:}\\
[/tex]
[tex]A=\sqrt{k^4(2+\sqrt5)(2+\sqrt5-\sqrt5+\sqrt3)(2+\sqrt5-\sqrt5-\sqrt3)(2+\sqrt5-4}\\
A=k^2\sqrt{(2+\sqrt5)(2+\sqrt3)(2-\sqrt3)(\sqrt5-2)}\\
A=k^2\sqrt{(4-5)(4-3)}\\
\boxed{A=k^2}\\
\text{Raza triunghiului circumscris unui triunghi este :}\\
\boxed{R=\dfrac{a\cdot b\cdot c}{4\cdot A}}\\
R=\dfrac{k^3(\sqrt5+\sqrt3)(\sqrt5-\sqr3)\cdot 4}{4k^2}=(5-3)k=2k\\
\text{Aria cercului circumscris este:}\\
\boxed{A_{cerc}=\pi\cdot R^2}\\
A_{cerc}=4k^2\cdot \pi\\
\text{Atunci:}\\
[/tex]
[tex]\dfrac{A}{A_{cerc}}=\dfrac{k^2}{4k^2\cdot \pi}=\boxed{\dfrac{1}{4\cdot \pi}}[/tex]
