Q. 124.1( 7 Votes )

# In the given figure, AB=AC and OB=OC. Prove that ∠ABO=∠ACO. Give that AB=AC and OB=OC.

Answer :

∆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

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