In Fig. 16.135, O is the centre of the circle, Bo is the bisector of ABC. Show that AB=AC.

Given that,

BO is the bisector of ABC


To prove: AB = BC


Proof: ABO = CBO (BO bisector of ABC) (i)


OB = OA (Radii)


Therefore,


ABO = DAB (Opposite angle to equal sides are equal) (ii)


OB = OC (Radii)


Therefore,


CBO = OCB (Opposite angles to equal sides are equal) (iii)


Compare (i), (ii) and (iii)


OAB = OCB (iv)


In triangle OAB and OCB, we have


OAB = OCB [From (iv)]


OBA = OBC (Given)


OB = OB (Common)


By AAS congruence rule



(By c.p.c.t)


Hence, proved


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