In figure below, AD bisects $\angle A$, $AB=12\ cm, AC=20\ cm$ and $BD=5\ cm$, determine CD.
"

Given:

AD bisects $\angle A$, $AB=12\ cm, AC=20\ cm$ and $BD=5\ cm$.

To do:

We have to determine CD.

Solution:

We know that,

The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the corresponding sides containing the angle.
Therefore,

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

$\frac{12}{20}=\frac{5}{CD}$

$CD=\frac{5\times20}{12}$

$CD=\frac{5\times5}{3}$

$CD=\frac{25}{3}$

$CD=8.33\ cm$

The length of $CD$ is $8.33\ cm$.

Tutorialspoint

Updated on: 10-Oct-2022

102 Views

Kickstart Your Career

Get certified by completing the course

Get Started