Question

In $△ABC,AE$ is the external bisector of $\angle A$, meeting BC produced at $E$. If $AB=10cm,AC=6cm$ and $BC=12cm$, then find $CE$

Answer 1

In $△ABC,AE$ is the external bisector of $\angle A$ meeting $BC$ produced at $E$.
Let $CE=xcm$. Now, by the angle bisector theorem, we have
$\frac{BE}{CE}=\frac{AB}{AC}\Rightarrow \frac{12+x}{x}=\frac{10}{6}$
$\Rightarrow 3(12+x)=5x$.
$\Rightarrow x=18$.
Hence, $CE=18cm$.