In ∆ABC with sides 8 cm, 9 cm, and 12 cm, the angle bisector of the largest angle divides the opposite sides into two segments. What is the length of the shorter segment?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 5 cm.
Suppose AB = 8, BC = 12 and AC = 9
Point D bisects ∠A.
As we know
DC/BD = 9/8
⇒ (DC/BD) + 1 = (9/8) + 1
⇒ (DC + BD)/BD = 17/8
12/BD = 17/8
BD = 96/17 cm or 5 cm