Question

In Fig. 4.57, 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.

Answer 1

In Fig. 4.57, AE is the bisector of the exterior ∠CAD meeting BC produced in E. If AB = 10 cm, AC = 6 cm and BC = 12 cm.

CE = 18 cm.

Given,

AE is the bisector of the exterior ∠CAD meeting BC produced in E.

AB = 10 cm

AC = 6 cm

BC = 12 cm

As we know that, the external bisector of an angle of a triangle divides the opposite sides externally in the ratio of the sides containing the angle.

So, we have the ratio

AB/AC  = BE/CE  

from figure, we have,

10/6  = (12+x)/x

10x  = 6(12+x)

10x  = 72 + 6x

10x - 6x = 72

4x = 72

x = 72/4

x = 18

Therefore, CE = 18 cm