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

SOLUTION :  

Given : AE is the bisector of the exterior ∠CAD meeting BC produced in E and AB = 10 cm, AC = 6 cm, and BC = 12 cm.

CE = x cm

BE = (12 + x) cm

Since AE is the bisector of the exterior ∠CAD.

So, BE/CE = AB/AC

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

(12+x)/x=10/6

6(12+x) = 10x

72 + 6x = 10x

10x - 6x = 72

4x = 72

x = 72/4

x = 18

Hence, CE = 18 cm

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Answer 2

Step-by-step explanation:

In ABC, AD is the bisector of ZA.

We know that, the internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.

For further solution see attachment