## RD Sharma Class 10 Solutions Chapter 7 Triangles Ex 7.3

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 7 Triangles Ex 7.3

**Other Exercises**

- RD Sharma Class 10 Solutions Chapter 7 Triangles Ex 7.1
- RD Sharma Class 10 Solutions Chapter 7 Triangles Ex 7.2
- RD Sharma Class 10 Solutions Chapter 7 Triangles Ex 7.3
- RD Sharma Class 10 Solutions Chapter 7 Triangles Ex 7.4
- RD Sharma Class 10 Solutions Chapter 7 Triangles Ex 7.5
- RD Sharma Class 10 Solutions Chapter 7 Triangles Ex 7.6
- RD Sharma Class 10 Solutions Chapter 7 Triangles Ex 7.7
- RD Sharma Class 10 Solutions Chapter 7 Triangles Revision Exercise
- RD Sharma Class 10 Solutions Chapter 7 Triangles VSAQS
- RD Sharma Class 10 Solutions Chapter 7 Triangles MCQS

**Question 1.**

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)**

**Solution:**

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

**Question 2.**

In the figure, 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.

**Solution:**

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)

**Question 3.**

In the figure, ∆ABC is a triangle such that \(\frac { AB }{ AC }\) = \(\frac { BD }{ DC }\) , ∠B = 70°, ∠C = 50°. Find ∠BAD.

**Solution:**

**Question 4.**

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

**Solution:**

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

**Question 5.**

In figure, AD bisects ∠A, AB = 12 cm AC = 20 cm, and BD = 5 cm. Determine CD.

**Solution:**

**Question 6.**

In the figure, In ∆ABC, if ∠1 = ∠2, prove that \(\frac { AB }{ AC }\) = \(\frac { BD }{ DC }\).

**Solution:**

Given : In ∆ABC,

AD is a line drawn from A meeting BC in D Such that ∠1 = ∠2

**Question 7.**

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

**Solution:**

In ∆ABC, AD, BE and CF are the bisector of ∠A, ∠B and ∠C respectively

AB = 5 cm, BC = 8 cm and CA = 4 cm

Hope given RD Sharma Class 10 Solutions Chapter 7 Triangles Ex 7.3 are helpful to complete your math homework.

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