MCQ
In a $\triangle\text{ABC},$ it is given that $AD$ is the internal bisector of $\angle\text{A}.$ If $AB = 10cm, AC = 14cm$ and $BC = 6cm,$ then $CD = ?$
- A$4.8cm$
- ✓$3.5cm$
- C$7cm$
- D$10.5cm$
✓
Answer
Correct option: B.
$3.5cm$
since $AD$ is the bisector of $\angle\text{A},$
by the angle bisector theorem,
$\frac{10}{14}=\frac{6-\text{x}}{\text{x}}$
$\Rightarrow10\text{x}=84-14\text{x}$
$\Rightarrow24\text{x}=84$
$\Rightarrow\text{x}=3.5$
So, $CD = 3.5cm$.
by the angle bisector theorem,
$\frac{10}{14}=\frac{6-\text{x}}{\text{x}}$
$\Rightarrow10\text{x}=84-14\text{x}$
$\Rightarrow24\text{x}=84$
$\Rightarrow\text{x}=3.5$
So, $CD = 3.5cm$.
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