In the given figure, AB=AC and OB=OC. Prove that ∠ABO=∠ACO. Give that AB=AC and OB=OC.
∆ABC and ∆OBC are isosceles triangle.
∴ ∠ABC = ∠ACB and ∠OBC = ∠OCB ….(1)
Also,
∠ABC = ∠ABO + ∠OBC
And ∠ACB = ∠ACO + ∠OCB
From 1 and above equations, we state that,
∠ABC = ∠ABO + ∠OBC
And ∠ABC = ∠ACO + ∠OBC
This implies that,
∠ABO = ∠ABC - ∠OBC
And ∠ACO = ∠ABC - ∠OBC
Hence,
∠ABO = ∠ACO = ∠ABC - ∠OBC