Có \(\frac{a}{sinA}=2R\Rightarrow a=2RsinA=2.\frac{7}{\sqrt{3}}.sin60°=7\)
Lại có \(S=pr\Rightarrow r=\frac{S}{p}=\frac{2S}{7+b+c}=\sqrt{3}\Rightarrow b+c=\frac{2S}{\sqrt{3}}-7\).
Theo định lí cosin ta có :
\(a^2=b^2+c^2-2bc.cosA\Leftrightarrow49=\left(b+c\right)^2-3bc\Leftrightarrow49.sinA=\left(b+c\right)^2.sinA-3bc.sinA\)\(\Leftrightarrow\frac{\sqrt{3}}{2}.49=\frac{\sqrt{3}}{2}\left(\frac{2S}{\sqrt{3}}-7\right)^2-6S\Leftrightarrow4\sqrt{3}S^2-120S=0\Leftrightarrow S=10\sqrt{3}\)
\(\Rightarrow Chuvi=2p=\frac{2S}{r}=\frac{2.10\sqrt{3}}{\sqrt{3}}=20\)
