Question
In figure, AD bisects $\angle\text{A},$ AB = 12cm, AC = 20cm, and BD = 5cm. Determine CD.
✓
Answer
In the $\triangle\text{ABC},$
AD is the bisector of $\angle\text{A}$
$\therefore\frac{\text{AB}}{\text{AC}}=\frac{\text{BD}}{\text{CD}}$
$\Rightarrow\frac{12}{20}=\frac{5}{\text{CD}}\Rightarrow\text{CD}=\frac{20\times5}{12}$
$\Rightarrow\text{CD}=\frac{25}{3}=8.33$
$\therefore\text{CD}=8.33$
AD is the bisector of $\angle\text{A}$
$\therefore\frac{\text{AB}}{\text{AC}}=\frac{\text{BD}}{\text{CD}}$
$\Rightarrow\frac{12}{20}=\frac{5}{\text{CD}}\Rightarrow\text{CD}=\frac{20\times5}{12}$
$\Rightarrow\text{CD}=\frac{25}{3}=8.33$
$\therefore\text{CD}=8.33$
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