Question

If ABC IS A TRIANGLE . BO AND CO ARE ANGLE BISECTOR OF ANGLE ABC AND ACB RESPECTIVELY. PROVE THAT ANGLE BOC=90+1/2ANGLE BAC​

Answer 1

Answer

∠ABO=∠OBC=X

AND

∠ACO=OCB=Y

In ΔABC, by angle sum property we have

2x + 2y + ∠A = 180°

⇒ x + y + (∠A/2) = 90°

⇒ x + y = 90° –  (∠A/2)  à (1)

In ΔBOC, we have

x + y + ∠BOC = 180°

90° – (∠A/2) + ∠BOC = 180° [From (1)]

∠BOC = 180° – 90° + (∠A/2)

∠BOC = 90° + (∠A/2)

Answer 2

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