Question

Se considera triunghiul ABC si AD bisectoarea unghiului BAC,D apartine (BC) si DE||AB,E apartine(AC).Daca AB=12 cm si AC=16 cm,calculati AE,DE,CE

Answer 1

Daca ED||AB, atunci <EDA≡<DAB (alterne interne) 
Dar , din Ipoteza stim ca <EAD≡<DAB=> 
<EAD≡<EDA⇒ΔEAD=isoscel ⇒ AE≡ED
Conform Thales:
$\frac{CE}{CA} = \frac{DE}{AB}$
⇒$\frac{CA-AE}{CA} = \frac{DE}{AB}$
Dar AE=DE⇒
$\frac{CA-DE}{CA} = \frac{DE}{AB}$
⇒$\frac{16-DE}{16} = \frac{DE}{12}$
12(16-DE)=16DE
192-12DE=16DE
192=28DE
DE=192/28
DE=48/7=AE
CE=AC-AE=16-48/7=112/7-48/7=64/7