In figure below, $AE$ is the bisector of the exterior $∠\ CAD$ meeting $BC$ produced in $E$. If $AB\ =\ 10\ cm$, $AC\ =\ 6\ cm$, and $BC\ =\ 12\ cm$, find $CE$.

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Given:

In the given figure, $AE$ is the bisector of the exterior $∠\ CAD$ meeting $BC$ produced in $E$.

$AB\ =\ 10\ cm$, $AC\ =\ 6\ cm$, and $BC\ =\ 12\ cm$.

To do:

We have to find the measure of $CE$.

Solution:

$AE$ is the bisector of $∠\ CAD$, this implies,

$\angle BAD=\angle CAD$

We know that,

The external bisector of an angle of a triangle divides the opposite side externally in the ratio of the sides containing the angle. 

Therefore,

$\frac{BE}{CE} = \frac{AB}{CA}$

$\frac{12+x}{x} = \frac{10}{6}$

$6(12+x) = 10(x)$

$72+6x = 10x$

$10x-6x=72$

$4x=72$

$x=\frac{72}{4}$

$x=18\ cm$

The measure of $CE$ is $18\ cm$.   

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Updated on: 10-Oct-2022

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