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Question -

ABC is a triangle. The bisector of the exterior angle at B and the bisector of ∠C intersect each other at D. Prove that ∠D = 1212 ∠A.



Answer -

In the given ΔABC, the bisectors of and intersect at D

We need to prove:

Now, using the exterior angle theorem,

∠ABE=∠BAC+∠ACB∠ABE=∠BAC+∠ACB   .….(1)

 As ∠ABE and ∠ACB are bisectedAs ∠ABE and ∠ACB are bisected

∠DCB=12∠ACB∠DCB=12∠ACB

Also,

∠DBA=12∠ABE∠DBA=12∠ABE

Further, applying angle sum property of the triangle

In  ΔDCB

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