RD Chapter 4- Triangles Ex-4.1 |
RD Chapter 4- Triangles Ex-4.2 |
RD Chapter 4- Triangles Ex-4.4 |
RD Chapter 4- Triangles Ex-4.5 |
RD Chapter 4- Triangles Ex-4.6 |
RD Chapter 4- Triangles Ex-4.7 |

In a ∆ABC, AD is the bisector of ∠A, meeting side BC at D.

(i) If BD = 2.5 cm, AB = 5 cm and AC = 4.2 cm, find DC. (C.B.S.E. 1996)

(ii) If BD = 2 cm, AB = 5 cm and DC = 3 cm, find AC. (C.B.S.E. 1992)

(iii) If AB = 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD. (C.B.S.E. 1992)

(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. (C.B.S.E. 1997C)

(vi) If AB = 5.6 cm, AC = 6 cm and DC = 3 cm, find BC. (C.B.S.E. 2001C)

(vii) If AD = 5.6 cm, BC = 6 cm and BD = 3.2 cm, find AC. (C.B.S.E. 2001C)

(viii) If AB = 10 cm, AC = 6 cm and BC = 12 cm, find BD and DC. (C.B.S.E. 2001)

**Answer
1** :

In ∆ABC, AD is the angle bisector of ∠A which meet BC at D

(i) BD = 2.5 cm, AB = 5 cm and AC = 4.2 cm

=> 6x = 10 (12 – x) = 120 – 10x

=> 6x + 10x = 120

=> 16x = 120

x = 7.5

BD = 7.5 cm and DC = 12 – 7.5 = 4.5 cm

**Answer
2** :

In ∆ABC, AE is the bisector of exterior ∠A which meets BC produced at E.

AB = 10 cm, AC = 6 cm, BC = 12 cm Let CE = x, then BE = BC + CE = (12 + x)

**Answer
3** :

In the figure, check whether AD is the bisector of ∠A of ∆ABC in each of the following :

(i) AB = 5 cm, AC = 10 cm, BD = 1.5 cm and CD = 3.5 cm

(ii) AB = 4 cm, AC = 6 cm, BD = 1.6 cm and CD = 2.4 cm

(iii) AB = 8 cm, AC = 24 cm, BD = 6 cm and BC = 24 cm

(iv) AB = 6 cm, AC = 8 cm, BD = 1.5 cm and CD = 2 cm

(v) AB = 5 cm, AC = 12 cm, BD = 2.5 cm and BC = 9 cm

**Answer
4** :
(i) AB = 5 cm, AC = 10 cm, BD = 1.5 cm, CD = 3.5 cm