Question

In figure, O is the centre of the circle, BO is the bisector of ∠ABC. Show that AB = AC.

Answer 1

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]