Question

In triunghiul ABC, (Ad bis <ABC, D€(BC), AB= 9 cm, AC= 15 cm si BC= 20 cm

Aflati BD si CD

Answer 1

Răspuns

Vezi atasament

Answer 2

Răspuns

Explicație pas cu pas:

$Pentru~a~simplifica~calculele,~voi~nota~BD~cu~x~si~CD~cu~y.\\Exercitiul~ne~sugereaza~sa~aplicam~teorema~bisectoarei :\\\dfrac{AB}{AC}=\dfrac{BD}{CD}\Rightarrow \dfrac{9}{15}=\dfrac{x}{y}\Rightarrow \dfrac{x}{9}=\dfrac{y}{15}=k\Rightarrow x=9k,y=15k\\D\in(BC)\Rightarrow BD+CD=BC\\9k+15k = 20\\24k=20\\k=\dfrac{20}{24}=\dfrac{5}{6}\\x=9k=9\cdot \dfrac{5}{6}=\dfrac{15}{2}\\y=15k=15\cdot \dfrac{5}{6}=\dfrac{25}{2}\\Prin~urmare~BD=\dfrac{15}{2}~cm~si~CD=\dfrac{25}{2}~cm.$