Question

[tran minh huy]

cho tam giac abc (ab>ac), ad la tia phan giac

so sanh dc va db

Answer 1

[zZz Cool Kid_new zZz]

A C B D a b c

Đặt AC=b;BC=a;AB=c

Theo tính chất đường phân giác ta có:

\(\frac{BD}{CD}=\frac{AB}{AC}=\frac{c}{b}\)

\(\Rightarrow\frac{BD}{CD}+1=\frac{c}{b}+1\)

\(\Rightarrow\frac{BD+CD}{CD}=\frac{c+b}{b}\)

\(\Rightarrow\frac{a}{CD}=\frac{c+b}{b}\)

\(\Rightarrow CD=\frac{ab}{b+c}\)

Khi đó \(BD=a-CD=a-\frac{ab}{b+c}=\frac{ac}{b+c}\)

Lại có:\(b< c\Rightarrow ab< ac\Rightarrow\frac{ab}{b+c}>\frac{ac}{b+c}\Rightarrow CD>BD\)