Question

In a triangle ABC ,the bisectors of angle Band angle C intersect each other at a point O. prove that angle BOC=90+1/2 angle A​

Answer 1

Consider ∆BOC.

∠1 + ∠2 + ∠BOC = 1800 ..(i)

In ∆ABC,

∠A + ∠B + ∠C = 1800

∠A + 2∠1 + 2∠2 = 1800

½ ∠A + ∠1 + ∠2 = 900

∠1 + ∠2 = 900 – ½ ∠A

Put above equation in (i), we get

900 – ½ ∠A + ∠BOC = 1800

∠BOC = 900 + ½ ∠A

Hence proved.