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# 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

Sujoy Das
06/02/2018 0 0

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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