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If O is any point inside △ABC, prove that ∠BOC > ∠A.

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Answer

If O is any point inside △ABC, prove that ∠BOC R.S. Aggarwal Mathematics Solutions ICSE Class 9.

Join OA, OB and OC, produce OA to meet BC at D.

In △AOB,

∠BOD > ∠BAO …..(1) (Exterior angle is greater than interior opposite angle)

In △AOC,

∠COD > ∠CAO …..(2) (Exterior angle is greater than interior opposite angle)

Adding eq.(1) and (2), we have:

∠BOD + ∠COD > ∠BAO + ∠CAO

⇒ ∠BOC > ∠BAC

⇒ ∠BOC > ∠A.

Hence, proved that ∠BOC > ∠A.

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