Question

In figure given below, O is the center of the circle, BO is the bisecter of /_ ABC. Ahow that AB=BC​

Answer 1

Answer:

Step-by-step explanation:Given: O is centre of circle

                                                       BO is bisector of /_ ABC

To proof : AB=BC

Proof : Since, BO is the bisector of ∠ABC, then,

 ∠ABO = ∠CBO …..(i)

From figure:

Radius of circle = OB = OA = OB = OC

∠OAB = ∠OCB …..(ii) [opposite angles to equal sides]

∠ABO = ∠DAB …..(iii) [opposite angles to equal sides]

From equations (i), (ii) and (iii),

we get  ∠OAB = ∠OCB …..(iv)  

In ΔOAB and ΔOCB:  ∠OAB = ∠OCB [From (iv)]

OB = OB [Common]

∠OBA = ∠OBC [Given]

Then, By AAS condition :

 ΔOAB ≅ ΔOCB  

So, AB = BC [By CPCT]