Question

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

Answer 1

An angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.

$\frac{AB}{AC}=\frac{BD}{CD}$ (1)

$AB=12cm$

$AC=20cm$

$BD=5cm$

So (1) becomes $\frac{12}{20}=\frac{5}{CD}$

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

$CD=8.33$

Hence $CD=8.33cm$