Q3 of 168 Page 4

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

We have


AB/AC=BD/DC


∴ ∠1=∠2


IN ⊿ABC


∠A+∠B+∠C=180


∠A+70+50=180


∠A+120=180


∠A=180-120


∠A=60


∠1+∠2=60 (∠1+∠2=∠A)


∠1+∠1=60 (∠1=∠2)


2∠1=60


∠1=60/2


∠1=30


∠BAD=30


More from this chapter

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1

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.

 2

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.

 4

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

 5

D, E and F are the points on sides BC, CA and AB respectively of such that AD bisects , BE bisects and CF bisects . If AB = 5 cm, BC = 8 cm and CA = 4 cm, determine AF, CE and BD.