Question

If $AD$ is internal angle bisector of $\angle BAC,BD:DC=2:3$, then find $AC:AB$.

Answer 1

Given that:

$BD:DC=2:3$ and $AD$ is internal angle bisector of $\angle BAC.$

By Angle Bisector Theorem,

$\frac{BD}{DC}=\frac{AB}{AC}$

$\Rightarrow \frac{AB}{AC}=\frac{2}{3}$

$\Rightarrow \frac{AC}{AB}=\frac{3}{2}$