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Question:
In a triangle ABC, AB = 8 units, BC = 10 units and CA = 12 units. AD is angle bisector of angle A and I is the incenter, find AI:ID.
Solution:
Solution : AB/AC = BD/CD (angle bisector theorem, as AD is angle bisector of angle A)
=> BD = 4 and CD = 6
Now, in triangle BAD, BI is angle bisector
=> BD/AB = DI/AI (angle bisector theorem)
=> AI/DI = 8/4 = 2/1
So, 2:1
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