Giải thích các bước giải:
a,
Ta có:
\(\begin{array}{l}
p = \frac{{AB + BC + CA}}{2} = \frac{{6 + 7 + 8}}{2} = \frac{{21}}{2}\\
{S_{ABC}} = \sqrt {p.\left( {p - AB} \right).\left( {p - BC} \right).\left( {p - CA} \right)} = \frac{{21\sqrt {15} }}{4}
\end{array}\)
Mặt khác, ta có:
\({S_{ABC}} = \frac{{AB.BC.CA}}{{4R}} \Rightarrow R = \frac{{AB.BC.CA}}{{4.{S_{ABC}}}} = \frac{{16\sqrt {15} }}{{15}}\)
b,
\(MA = 2MB \Rightarrow MB = \frac{1}{3}AB \Rightarrow {S_{MBC}} = \frac{1}{3}{S_{ABC}} = \frac{{7\sqrt {15} }}{4}\)