Question

O is the centre of the circle, BO is the bisector of angle ABC. Show that AB= AC​

Answer 1

Answer:

BO is bisector of angle ABC then,

angle ABO=angle CBO.........,(1)

radius of circles=OB=OA=OB=OC

angle OAB=angle OCB........(2). (opposite angle to equal side)

angle ABO=angle DAB.........(3). ( ,,)

from equation (1) (2) (3), we get

angle OAB=angle OCB....(4)

In triangle OAB And triangle OCB

angle OAB=angle OCB (from 4)

OB=OB.....( common)

angle OBA=angle OBC....(given)

by AAS condition

triangle OAB= triangle OCB

So AB=AC ...(by cpct)