Question

In triunghiul ABCD ,AD bisectoarea lui ABC,D apartine (BC) ,AB=9 cm AC=15 cm si BC=20 cm.Aflati BD si CD .

Answer 1

Enunț:

In triunghiul ABC, AD este bisectoarea unghiului BAC, D∈ BC, 

AB  = 9 cm, AC = 15 cm,  BC = 20 cm. Aflati BD si CD.

R:

Aplicăm teorema bisectoarei :

[tex]\dfrac{BD}{CD}=\dfrac{AB}{AC}\Rightarrow \dfrac{BD}{CD}=\dfrac{9}{15}\stackrel{derivare}{\Longrightarrow}\ \dfrac{BD}{CD+BD}=\dfrac{9}{15+9}\\\;\\ \dfrac{BD}{BC}=\dfrac{9}{24}\Longrightarrow \dfrac{BD}{20}=\dfrac{9}{24}\\\;\\ BD=\dfrac{9\cdot 20}{24} \Longrightarrow BD = 7,5\ cm[/tex]

CD = BC - BD = 20 - 7,5 = 12,5 cm