Question

In ABC, Ad is the angle bisector of the angle A. If AB=3, AC=6 and BC=33, then AD is:​

Answer 1

Step-by-step explanation:

In a triangle ABC, AD is the bisector of angle A. If AB =3 AC=6 and BC=3√3. What is the length of AD?

In ∆ABC AD is bisector of angleA

Here AB=3 AC=6 and BC=3√3

Now AB/AC=3/6=1/2

According to angle bisector law BD/DC should be 1/2

Since BC=3√3 therefore BD=√3 and DC=2√3

Then we have BD/DC=√3/2√3=1/2

Again here AB^2 +BC^2=AC^2

Therefor it is a right angle traingle and angle B=90°

Hence from right angle ∆ABD we have

AD^2=AB^2+BD^2

Or, AD^2=(3)^2+(√3)^2

Or, AD^2=9+3

Or, AD^2=12

Or, AD=√12

Or, AD=2√3