Question

ad is the bisector of angle bac in triagngle abc.if ab is equal to 10cm and ac is equal to 6cm and bc is equal to 12cm then bd is equal to​

Answer 1

Step-by-step explanation:

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