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Oct 2, 2013

# Bisectors of angles B and C of a triangle ABC intersect each other at O .

Bisectors  of angles B and C of a triangle ABC intersect each other at the point O . prove

Agam Gupta

Member since Sep 21, 2013

 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)

Kishore Kumar

Member since

 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)
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