Q13 of 95 Page 5

In the adjoining figure, AD is the bisector of ∠BAC. If BC = 10 cm, BD = 6 cm AC = 6 cm, then find AB.


Given: AD is the bisector of BAC


and by Angle-Bisector theorem which states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides.





⇒ AB = 3.6cm


More from this chapter

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11

If D and E are points on sides AB and AC respectively of ΔABC and AB = 12 cm, AD = 8 cm, AE = 12 cm, AC =18 cm, then prove that DE || BC.

 12

P and Q are points on sides AB and AC respectively of Δ ABC. For each of the following cases, state whether PQ || BC.

(i) AP= 8 cm, PB = 3 cm, AC = 22 cm and AQ =16 cm.


(ii) AB= 1.28 cm, AC = 2.56 cm, AP= 0.16 cm and AQ = 0.32 cm


(iii) AB = 5 cm, AC =10 cm, AP= 4 cm, AQ = 8 cm.


(iv) AP= 4 cm, PB= 4.5 cm, AQ = 4 cm, QC = 5 cm.

 14

In the adjoining figure, AD is the bisector of ∠BAC. If AB = 10 cm, AC = 6 cm, BC = 12 cm, find BD.

 15

In EABC, AD is the bisector of ∠A. If AB = 3.5 cm, AC = 4.2 cm, DC = 2.4 cm. Find BD.