[tex]\it AC\cap BD=\{O\} \Rightarrow AO=OC\ \ \ \ \ (1)\\ \\ \left.\begin{aligned} \it O-mijlocul\ lui \ BD\\ \\ N-mijlocul\ lui\ CD\end{aligned}\right\} \Rightarrow ON-linie\ mijlocie\ \hat\imath n\ \Delta BCD \Rightarrow \\ \\ \\ \Rightarrow \begin{cases}\ \it ON||BC \Rightarrow ON||MC\\ \\ ON=\dfrac{BC}{2} \Rightarrow ON=MC\end{cases} \Rightarrow OMCN-paralelogram[/tex]
[tex]\it Fie\ MN\cap OC=\{F\} \Rightarrow FM=FN \Rightarrow AF-median\breve a\ \hat\imath n\ \Delta\ AMN\ \ \ (2)\\ \\ MN\cap OC=\{F\} \Rightarrow OF=\dfrac{OC}{2}\ \stackrel{(1)}{=}\ \dfrac{AO}{2}\ \ \ \ \ (3)\\ \\ \\ (2),\ (3) \Rightarrow O\ =\ centrul\ de\ \ greutate\ pentru\ \Delta AMN[/tex]
