Q10 of 62 Page 180

Check whether AD is the bisector of ∠A of ΔABC in each of the following.

AB = 4 cm, AC = 6 cm, BD = 1.6 cm, and CD = 2.4 cm.

Given: AB = 4 cm, AC = 6 cm, BD = 1.6 cm, and CD = 2.4 cm


Required: To verify if AD is the bisector of ∠A of ΔABC


Consider the ΔABC,


Here, and


Here, we can clearly see that


∴We can say that AD is the angle bisector of ∠A using Converse angle bisector theorem.


∴ Yes, AD is the angle bisector of ∠A


More from this chapter

All 62 →
9

In a ΔABC, AD is the internal bisector of ∠A, meeting BC at D.

If AB = 5.6 cm, AC = 6 cm and DC = 3 cm find BC.

 9

In a ΔABC, AD is the internal bisector of ∠A, meeting BC at D.

If AB = x, AC = x–2, BD = x + 2 and DC = x–1 find the value of x.

 10

Check whether AD is the bisector of ∠A of ΔABC in each of the following.

AB = 6 cm, AC = 8 cm, BD = 1.5 cm and CD = 3 cm.

 11

In a ΔMNO, MP is the external bisector of ∠M meeting NO produced at P. If MN = 10 cm, MO = 6 cm, NO = 12 cm, then find OP.