Đáp án:
$\begin{array}{l}
Theo\,Pytago:\\
B{C^2} = A{B^2} + A{C^2}\\
= {6^2} + {8^2} = 100\\
\Rightarrow BC = 10\left( {cm} \right)\\
Theo\,t/c:\\
\dfrac{{BD}}{{AB}} = \dfrac{{CD}}{{AC}} = \dfrac{{BD + CD}}{{AB + AC}} = \dfrac{{BC}}{{6 + 8}} = \dfrac{{10}}{{14}} = \dfrac{5}{7}\\
\Rightarrow \left\{ \begin{array}{l}
BD = \dfrac{5}{7}.AB = \dfrac{5}{7}.6 = \dfrac{{30}}{7}\\
CD = \dfrac{5}{7}.AC = \dfrac{5}{7}.8 = \dfrac{{40}}{7}
\end{array} \right.\\
Vậy\,BC = 10;BD = \dfrac{{30}}{7};CD = \dfrac{{40}}{7}
\end{array}$
