Giải thích các bước giải:
\(\begin{array}{l}
a,\\
p = \frac{{AB + BC + CA}}{2} = \frac{{6 + 8 + 11}}{2} = \frac{{25}}{2}\\
{S_{ABC}} = \sqrt {p\left( {p - AB} \right)\left( {p - BC} \right)\left( {p - CA} \right)} = \frac{{15\sqrt {39} }}{4}\\
b,\\
\cos B = \frac{{B{A^2} + B{C^2} - A{C^2}}}{{2.BA.BC}} = \frac{{{6^2} + {{11}^2} - {8^2}}}{{2.6.11}} = \frac{{31}}{{44}}\\
\Rightarrow \widehat B = 45,2^\circ \\
{S_{ABC}} = \frac{{AB.BC.CA}}{{4R}}\\
\Leftrightarrow \frac{{15\sqrt {39} }}{4} = \frac{{6.8.11}}{{4R}}\\
\Rightarrow R = \frac{{528}}{{15\sqrt {39} }}\\
c,\\
{m_C}^2 = \frac{{{a^2} + {b^2}}}{2} - \frac{{{c^2}}}{4}\\
\Leftrightarrow {m_C}^2 = \frac{{{6^2} + {8^2}}}{2} - \frac{{{{11}^2}}}{4}\\
\Leftrightarrow {m_C}^2 = \frac{{79}}{4}\\
\Leftrightarrow {m_C} = \frac{{\sqrt {79} }}{2}
\end{array}\)
