Đáp án: ${BC = 15cm;DB = \frac{{45}}{7}\left( {cm} \right);DC = \frac{{60}}{7}\left( {cm} \right)}$
Giải thích các bước giải:
Theo Pytago ta có:
$\begin{array}{l}
B{C^2} = A{B^2} + A{C^2} = {9^2} + {12^2} = 225\\
\Rightarrow BC = 15\left( {cm} \right)\\
Theo\,t/c\,ta\,co:\\
\frac{{DB}}{{AB}} = \frac{{DC}}{{AC}}\\
\Rightarrow \frac{{DB}}{9} = \frac{{DC}}{{12}} = \frac{{DB + DC}}{{9 + 12}} = \frac{{BC}}{{21}} = \frac{{15}}{{21}} = \frac{5}{7}\\
\Rightarrow \left\{ \begin{array}{l}
DB = \frac{{45}}{7}\left( {cm} \right)\\
DC = \frac{{60}}{7}\left( {cm} \right)
\end{array} \right.
\end{array}$
