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MissMarry13
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Medianele AM si BN ale triunghiului ABC se intersecteaza in punctul O.Calculati:
a)AO si BO,daca AM=9cm,BN=12cm;
b)AM si BN,daca AO=4√ 3cm,BO=6√ 3cm;
c)OM si ON,daca AM=12cm,BN=15cm;
d)AO si BO,daca OM=√ 5cm,On=√ 6cm;

Dau coroana si cite puncte vreti!
URGENT!!!

Răspuns :

Mikkka
daca AM si BN -mediane â‡’ AM n BN = {G} -centrul de greutate
⇒ AO=2/3 * AM  ;  OM=1/3 *AM ;
AM= 3*AO/2  ;  AM=3*OM si AO=2*ON
BO=2/3*BN  ;  ON=1/3*BN ;
 BN=3*BO/2  ; BN= 3*ON si BO=2*ON

a) AM = 9 cm ⇒ AO=2*9:3=6 cm
BN=12 cm â‡’ BO=2*12:3=8 cm

b) AM=3*4√3 :2=6√3 cm
BN=3*6√3:2=  9√3 cm

c) OM= 12:3=4 cm
ON=15:3=5 cm

d) AO= 2*√5= 2√5cm
BO = 2√6cm

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