Question

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Answer 1

To prove angle BOC = 90°+1/2 ∡ A

Proof: In triangle ABC

∡ A+ ∡ B + ∡ C = 180° ( by angle sum property)

∡ A + 2∡ OBC+ 2∡ OCB =180°

2( ∡ OBC+ ∡ OCB) =180°-∡ A

∡ OBC + ∡ OCB = 180°/2-∡ A/2

∡ OBC + ∡ OCB = 90°- A/2

Now in triangle BOC

∡ BOC + ∡ OBC + ∡OCB = 180° ( by angle sum property)

∡ BOC = 180° - ( ∡OBC+ ∡ OCB)

∡ BOC = 180° - (90°-∡A/2)

∡ BOC = 180°-90°+∡ A/2

∡ BOC = 90°+∡ A/2

PROVED

Hope this will help you