Mathematics

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


ANSWER


SOLUTION
Given that:
$$BD:DC=2:3$$ and $$AD$$ is internal angle bisector of $$\angle BAC.$$
By Angle Bisector Theorem,
$$\cfrac{BD}{DC}=\cfrac{AB}{AC}$$
$$\Rightarrow \cfrac{AB}{AC}=\cfrac23$$
$$\Rightarrow \cfrac{AC}{AB}=\cfrac32$$
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