Q4 of 186 Page 184

In a ΔABC, AD is the bisector of ∠A.


If AB = 5.6 cm, BD = 3.2 cm and BC = 6 cm, find AC.

Given: AB = 5.6 cm, BC = 6 cm and BD = 3.2 cm

Since AD bisects ∠A, we can apply angle-bisector theorem in ∆ABC,



Substituting given values, we get



Here, DC is given by


DC = BC – BD


⇒ DC = 6 – 3.2 = 2.8



⇒


⇒ AC = 4.9


Thus, AC is 4.9 cm.


More from this chapter

All 186 →
4

In a ΔABC, AD is the bisector of ∠A.


If AB = 6.4 cm, AC = 8 cm and BD = 5.6 cm, find DC.

 4

In a ΔABC, AD is the bisector of ∠A.


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

 4

In a ΔABC, AD is the bisector of ∠A.


If AB = 5.6 cm, AC = 4 cm and DC = 3 cm, find BC.

 5

M is a point on the side BC of a parallelogram ABCD. DM, when produced, meets AB produced at N. Prove that


(i) (ii)