Question

In a triangle ABC, AD is the bisector of angle A.
(ii) If AB = 5.6 cm, BD=3.2 cm and BC = 6 cm,
find AC
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Answer 1

Given:

Δ ABC and AD bisects ∠A, meeting side BC at D. And AB = 5.6 cm, BC = 6 cm, and BD = 3.2 cm.

To find: AC

Proof - Since, AD is the bisector of ∠ A meeting side BC at D in Δ ABC

⇒ AB/ AC = BD/ DC

5.6/ AC = 3.2/ DC

And, we know that

BD = BC – DC

3.2 = 6 – DC

∴ DC = 2.8 cm

⇒ 5.6/ AC = 3.2/ 2.8

AC = (5.6 x 2.8)/ 3.2

∴ AC = 4.9 cm