Question

In △ABC, BD is the internal bisector of ∠B meeting AC at D. If CD = 7 cm and AC = 10.5 cm, then AB : BC is

• A. 2 : 3
• B. 1 : 2
• C. 3 : 4
• D. 3 : 2

Answer 1

The Correct Option is B

In triangle △ABC, BD is the internal bisector of ∠B meeting AC at D. Given that CD = 7 cm and AC = 10.5 cm, we are to find the ratio AB : BC.

To find this ratio, we apply the angle bisector theorem, which states that an angle bisector of a triangle divides the opposite side into segments proportional to the other two sides. Therefore, according to the angle bisector theorem, we have:

AB/BC = AD/DC

First, calculate AD:

AC = AD + DC

10.5 = AD + 7

Solving for AD, we find:

AD = 10.5 - 7 = 3.5 cm

Now, substitute AD and DC into the angle bisector theorem equation:

AB/BC = 3.5/7

Simplifying 3.5/7 to its lowest terms gives:

AB/BC = 1/2

Therefore, the ratio AB : BC is 1 : 2.