Question
In figure, $AD$ bisects $\angle\text{A}, AB = 12\ cm, AC = 20\ cm, $ and $BD = 5\ cm.$ 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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