Question

in triangle ABC , AD is the bisector of angle A meeting side BC at D. If AB is equal to 3.5 cm AC is equal to 4.2 cm and BC equal to 2.8 cm find BD​

Answer 1

Given in △ABC, AD is the bisector of angle A

By internal angle bisector theorem, the bisector of vertical angle of a triangle divides the base in the ratio of the other two sides.

(i)

AC

AB = DC BD

4.2

5 =

DC

2.5

DC= 5 2.5×4.2

∴ DC=2.1cm

(ii)

AC

AB =

DC

BD

AC

5

=

3

2

∴ AC=

2

5×3

∴ AC=7.5cm