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

If D and E are points on sides AB and AC respectively of a such that and BD = CE. Prove that is isosceles.

In a , AD is the bisector of , meeting side BC at D.

(i) If BD = 2.5 cm, AB = 5 cm and AV = 4.2 cm, find DC.

(ii) If BD = 2 cm, AB = 5 cm and DC = 3 cm, find AC.

(iii) If AB = 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.

(iv) If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC.

(v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm, find AB.

(vi) If AB = 5.6 cm, AC = 6 cm and DC = 6 cm, find BC.

(vii) If AD = 5.6 cm, BC = 6 cm and BD = 3.2 cm, find AC.

(viii) If AB = 10 cm, AC = 6 cm and BC = 12 cm, find BD and DC.

In Fig. 4.58, is a triangle such that , . Find.

In (fig. 4.59), if , prove that .