Question

In ∆ ABC . AD is the bisector of angle A . If BC = 10cm BD = 6cm AC = 6cm. find AB​

Answer 1

Answer:

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.

∴

DB

CD

=

AB

AC

⟹

BC−CD

CD

=

10

6

⟹

CD(

CD

BC

−1)

CD

=

10

6

⟹

CD

BC

=

6

10

+1

⟹

CD

12

=

9

16

CD=

2

9

=4.5cm

And BC−CD=DB

12−4.5=DB

DB=7.5cm