Question

In triunghiul ABC(AD bisectoare ABC,D e (BC),AB=9cm,AC=15 cm si BC=20 cm.Aflati BD si CD.URGENT

Answer 1

Din teorema bisectoarei, avem:

$\dfrac{BD}{DC}=\dfrac{AB}{AC}\Rightarrow \dfrac{DB}{20-DB}=\dfrac{9}{15}$ Adunam numaratorii la numitori, si obtinem:

$\dfrac{DB}{20}=\dfrac{9}{24}\Rightarrow DB=\dfrac{20\cdot9}{24}=7,5\ cm\Rightarrow DC=20-7,5=12,5\ cm$