Question

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​

Answer 1

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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