[tex]\triangle ABC \; : \; AE \cap BF \cap CD = \{ G\}[/tex]
[tex]a)\, AE \, - \, mediana \Rightarrow AG = \dfrac{2}{3}AE=\dfrac{2}{3} \cdot 8 = \dfrac{16}{3}\\\;[/tex]
[tex]b)\, CD \, - \, med \Rightarrow GD = \dfrac{1}{3} CD \Rightarrow \dfrac{4}{1} =\dfrac{CD}{3} \Rightarrow CD=12 \\\;[/tex]
[tex]c)\, BF \, -\, med \Rightarrow BG = \dfrac{2}{3}BF \Rightarrow \dfrac{10}{1} = \dfrac{2BF}{3} \Rightarrow BF = \dfrac{10 \cdot 3}{2} = 15\\\;[/tex]
[tex]d) \, AE \,-\, med \Rightarrow GE = \dfrac{1}{3}AE \Rightarrow \dfrac{3}{1}=\dfrac{AE}{3} \Rightarrow AE = 9\\AG = \dfrac{2}{3} AE \Rightarrow AG = \dfrac{2}{3} \cdot 9 \Rightarrow AG=6[/tex]
[tex]Gliseaza \;spre \;dreapta \;pentru \;a \;vizualiza\; raspunsul \;complet.[/tex]
