# In Fig. 6.63, D is a point on side BC of ∆ABC such that BD/CD = AB/AC. Prove that: AD is the bisector of ∠BAC

**Solution:**

Extended BA to E such that AE = AC and join CE.

In ∆AEC

AE = AC ⇒ ∠ACE = ∠AEC_____(i)

It is given that

BD/CD = BA/CA

BD/CD = BA CD/AE (AC = AE)____(ii)

In ∆ABD and ∆EBC

AD || EC (Converse of Basic Proportionality Theorem)

⇒ ∠BAD = ∠BEC (Corresponding angles)______(iii)

and ∠DAC = ∠ACE (Alternate interior angles)______(iv)

From (i), (iii) and (iv)

∠BAD = ∠DAC

⇒ AD is the bisector of ∠BAC

**Video Solution:**

## In Fig. 6.63, D is a point on side BC of ∆ABC such that BD/CD = BA/CA. Prove that: AD is the bisector of ∠BAC.

### NCERT Class 10 Maths Solutions - Chapter 6 Exercise 6.6 Question 9:

In Fig. 6.63, D is a point on side BC of ∆ABC such that BD/CD = BA/CA. Prove that: AD is the bisector of ∠BAC

In the above figure, D is a point on side BC of ∆ABC such that -BD/CD = BA/CA. Hence proved that AD is the bisector of ∠BAC