[tex]\it \dfrac{ME}{MB}= \dfrac{1}{3} \Rightarrow \dfrac{ME}{MB-ME}= \dfrac{1}{3-1} \Rightarrow \dfrac{ME}{EB}= \dfrac{1}{2}\ \ \ \ \ (1) \\ \\ \\ DA=MA-MD=24-8=16\\ \\ \\ \dfrac{MD}{DA}= \dfrac{\ 8^{(8}}{16} = \dfrac{1}{2} \ \ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow \dfrac{ME}{EB}= \dfrac{MD}{DA} \stackrel{R.T.Thales}{\Longrightarrow} DE||AB\ \ \ \ \ (3)\\ \\ \\ AB\subset \alpha \ \ \ \ \ (4) \\ \\ \\ (3),\ (4) \Rightarrow DE|| \alpha[/tex]
[tex]\it \rule{90}{0.3}\\ \\ DE||AB \stackrel{T.f.a}{\Longrightarrow}\Delta MDE \sim \Delta MAB \Rightarrow \dfrac{MD}{MA}= \dfrac{DE}{AB} \Rightarrow \dfrac{8}{24}= \dfrac{DE}{30} \Rightarrow \\ \\ \\ \Rightarrow DE=\dfrac{8\cdot30}{24}=\dfrac{240}{24}=10\ cm[/tex]
