MCQ
In a $\triangle\text{ABC}$ it is given that $AD$ is the internal bisector of $\angle\text{A}.$ If $BD = 4\ cm, DC = 5\ cm$ and $AB = 6\ cm,$ then $AC =?$
- A$4.5\ cm$
- B$8\ cm$
- C$9\ cm$
- ✓$7.5\ cm$
✓
Answer
Correct option: D.
$7.5\ cm$
since $AD$ is the bisector of $\angle\text{A},$
by the angle bisector theorem,
$\frac{\text{AB}}{\text{AC}}=\frac{\text{BD}}{\text{DC}}$
$\Rightarrow\frac{6}{\text{x}}=\frac{4}{5}$
$\Rightarrow\text{x}=7.5\text{ cm}$
So $, AC = 7.5\ cm.$
by the angle bisector theorem,
$\frac{\text{AB}}{\text{AC}}=\frac{\text{BD}}{\text{DC}}$
$\Rightarrow\frac{6}{\text{x}}=\frac{4}{5}$
$\Rightarrow\text{x}=7.5\text{ cm}$
So $, AC = 7.5\ cm.$
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