Question

$AD$ is angular bisector of $△ABC$ such that $BD:DC=2:3.$ If $AB=7$ cm, what is $AC:BC?$

• A. $2:3$
• B. $3:2$
• C. $21:10$
• D. None of these

Answer 1

The correct option is C $21:10$

$AD$ is angular bisector,
By internal angle bisector theorem,
$\frac{AB}{AC}=\frac{BD}{DC}$
$\frac{7}{AC}=\frac{2}{3}$
$AC=\frac{21}{2}$
Now, $\frac{AC}{BC}=\frac{\frac{21}{2}}{5}=\frac{21}{10}$