Question

In triangle ABC, OB and OC are the bisectors of angle B and Angle C respectively. Prove that OB=OC

Answer 1

Answer:

If ∆abc is an isosceles triangle then-

AB=AC

Angle ABC = Angle ACB

Angle OBC = 1/2Angle ABC

Angle OCB =1/2 Angle ACB

Therefore, Angle ABC = Angle ACB

1/2Angle ABC =1/2 Angle ACB

Angle OBC = Angle OCB

Therefore,OC=OB