Đáp án:
a) Ta có:
$\begin{array}{l}
\frac{{AB}}{{BC}} = \frac{6}{9} = \frac{2}{3};\frac{{BC}}{{BD}} = \frac{9}{{6 + 7,5}} = \frac{2}{3}\\
\Rightarrow \frac{{AB}}{{BC}} = \frac{{BC}}{{BD}} = \frac{2}{3}\\
Xét\,\Delta ABC;\Delta CBD\,co:\\
+ \widehat {ABC}\,chung\\
+ \frac{{AB}}{{BC}} = \frac{{BC}}{{BD}} = \frac{2}{3}\\
\Rightarrow \Delta ABC \sim \Delta CBD\left( {c - g - c} \right)\\
b)Do:\Delta ABC \sim \Delta CBD\\
\Rightarrow \frac{{AB}}{{BC}} = \frac{{AC}}{{CD}}\\
\Rightarrow CD = 11,25\left( {cm} \right)
\end{array}$