Question

if the bisector of Angle B and angle C of a triangle ABC meet at point O then prove that angle BOC is equals to 90 degree + half of angle A

Answer 1

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Agam answered 7 month(s) ago

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 <BOC= 90°+1/2 <A
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)