Fie AM = a ⇒ AB = 2a ⇒ DC = AB = 2a
[tex]\it \begin{cases}\it AB||DC\\ \\ M\in AB\end{cases} \Rightarrow AM||DC\stackrel{T.f.a.}{\Longrightarrow }\ \ \Delta OMA\sim \Delta ODC \Rightarrow \dfrac{OM}{OD}=\dfrac{AM}{DC} \Rightarrow\\ \\ \\ \Rightarrow\dfrac{OM}{OD+OM}=\dfrac{AM}{DC+AM} \Rightarrow \dfrac{OM}{DM}=\dfrac{x}{2x+x} \Rightarrow \dfrac{OM}{6}=\dfrac{x}{3x} \Rightarrow\\ \\ \\ \Rightarrow \dfrac{OM}{6}=\dfrac{^{2)}1}{\ 3} \Rightarrow \dfrac{OM}{6} =\dfrac{2}{6} \Rightarrow OM=2\ cm[/tex]
