Question

Medianele [AE] [BF] [CD] ale triunghiului ABC sunt congruente in G. ( E € BC , F € AC , D € AB)
a) AG daca AE =8 cm
b) CD daca GD =4 cm
c) GF daca BG=10 cm
d) GA daca GE = 3 cm​

Answer 1

$\triangle ABC \; : \; AE \cap BF \cap CD = \{ G\}$

$a)\, AE \, - \, mediana \Rightarrow AG = \dfrac{2}{3}AE=\dfrac{2}{3} \cdot 8 = \dfrac{16}{3}\\\;$

$b)\, CD \, - \, med \Rightarrow GD = \dfrac{1}{3} CD \Rightarrow \dfrac{4}{1} =\dfrac{CD}{3} \Rightarrow CD=12 \\\;$

$c)\, BF \, -\, med \Rightarrow BG = \dfrac{2}{3}BF \Rightarrow \dfrac{10}{1} = \dfrac{2BF}{3} \Rightarrow BF = \dfrac{10 \cdot 3}{2} = 15\\\;$

$d) \, AE \,-\, med \Rightarrow GE = \dfrac{1}{3}AE \Rightarrow \dfrac{3}{1}=\dfrac{AE}{3} \Rightarrow AE = 9\\AG = \dfrac{2}{3} AE \Rightarrow AG = \dfrac{2}{3} \cdot 9 \Rightarrow AG=6$

$Gliseaza \;spre \;dreapta \;pentru \;a \;vizualiza\; raspunsul \;complet.$