Question

consideram triunghiul ABC si punctele D £(AB) . E £(AC) astfel ıncat DE ıı BC sı ADsupraAB=3supra5 calculati valorea rapoartelor AD supra DB. AE supra EC. AC supra EC. AE supra AC

Answer 1

Enunt:

Se considera triunghiul ABC si punctele D∈(AB), E∈(AC),

astfel incat DE||BC  si AD/AB=3/5.

Determinati valoarea rapoartelor :

AD/DB,  AE/EC,  AC/EC,  AE/AC.

Rezolvare:

$\dfrac{AD}{AB}=\dfrac{3}{5} \stackrel{derivare}{\Longrightarrow}\ \dfrac{AD}{AB-AD}=\dfrac{3}{5-3} \Longrightarrow \dfrac{AD}{DB}=\dfrac{3}{2}$

$DE || BC \stackrel{T. Thales}{\Longrightarrow}\ \dfrac{AE}{EC}=\dfrac{AD}{DB}=\dfrac{3}{2}$

[tex]\dfrac{AE}{EC}=\dfrac{3}{2}\stackrel{derivare}{\Longrightarrow} \ \dfrac{AE+EC}{EC}=\dfrac{3+2}{2} \Longrightarrow\\\;\\ \Longrightarrow \dfrac{AC}{EC}=\dfrac{5}{2}[/tex]