in an isosceles triangle ABC with ab is equal to AC the bisectors of Angle B and angle C intersect each other at O join it to Osho that AB is equal to AC and A bisects Angle A
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Since,
AB=AC..........(1)
OB is the bisector of ∠B
So, ∠ABO=∠OBC=21∠B.......(2)
OC is the bisector of ∠C
So, ∠ACO=∠OCB=21∠C.......(3)
⇒∠ACB=∠ABC (Angles opposite to equal sides are equal)
21∠ACB=21∠ABC
∠OCB=∠OBC From (2) and (3)
Hence,
OB=OC (Sides opposite to equal angles are equal)
Hence proved.
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