In figure, AE is the bisector of exterior ∠CAD, meeting . . .

Question : In figure, AE is the bisector of exterior ∠CAD, meeting BC produced in E. If AB = 10 cm, AC = 6 cm, and BC = 12 cm, then CE equal to 
a) 5 cm 

b) 15 cm 

c) 18 cm 

d) 28 cm 

Doubt by Saumya 

Hint : Use External Angle Bisector Theorem

Solution : 

AE is the bisector of exterior ∠CAD

i.e. ∠DAE = ∠CAE (Given)

BE/CE=AB/AC (Exterior Angle Bisector Theorem) 

AB = 10 cm 

AC = 6 cm

BC = 12 cm

CE = ?

BE/CE=AB/AC

(BC+CE)/CE = AB/AC

(12+CE)/CE=10/6
(12+CE)/CE=5/3
36+3CE = 5CE
36 = 5CE-3CE
36 = 2CE
36/2 = CE
18 = CE
CE = 18 cm

Hence, c) would be the correct option.