\(r=\left(p-a\right)tan\frac{A}{2}=\left(p-b\right)tan\frac{B}{2}=\left(p-c\right)tan\frac{C}{2}\)
\(\Rightarrow\frac{5\sqrt{3}}{3}=\frac{b+c-a}{2}.tan30^0\Leftrightarrow\frac{5\sqrt{3}}{3}=\frac{b+c-10}{2}.\frac{\sqrt{3}}{3}\)
\(\Rightarrow b+c=20\) \(\Rightarrow p=\frac{a+b+c}{2}=15\)
Mặt khác \(R=\frac{a}{2sinA}=\frac{10}{\sqrt{3}}=\frac{10\sqrt{3}}{3}\)
\(S=\frac{abc}{4R}\) ; \(S=pr\Rightarrow\frac{abc}{4R}=pr\)
\(\Leftrightarrow\frac{10.bc}{4.\frac{10}{\sqrt{3}}}=p.\frac{5\sqrt{3}}{3}\Leftrightarrow bc=\frac{20p}{3}=100\)
\(\Rightarrow\left\{{}\begin{matrix}b+c=20\\bc=100\end{matrix}\right.\) theo Viet đảo b;c là nghiệm:
\(x^2-20x+100=0\Leftrightarrow x=10\Rightarrow b=c=10\)
