[tex]\it DE||BC \stackrel{T.f.a.}{\Longrightarrow}\ \Delta ABC\sim\Delta ADE \Rightarrow \dfrac{AB}{AD}=\dfrac{BC}{DE}=\dfrac{AC}{AE} \Rightarrow \\ \\ \\ \Rightarrow\dfrac{15}{AD}=\dfrac{10}{6}=\dfrac{AC}{AC-8} \Rightarrow \begin{cases} \it \dfrac{15}{AD}=\dfrac{10}{6} \Rightarrow AD=\dfrac{6\cdot15}{10}=\dfrac{90}{10}=9\ cm\\ \\ \\ \it \dfrac{10}{6}=\dfrac{AC}{AC-8} \Rightarrow 10AC-80=6AC \Rightarrow AC=20\end{cases}[/tex]
[tex]\it BD=AB-AD=15-9=6\ cm[/tex]
