In ∆ ABC , the bisector of ∆B and ∆C meets at O . prove that ∆ BOC =90° + ∆ A /2.
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In Triangle BOC:
/_BOC = 180 - 1/2(/_B + /_C) [Angle Sum Property of a triangle]
=> /_B + /_C = 360 - 2/_BOC
In Triangle ABC:
/_B + /_C = 180 - /_A [Angle Sum Property of a triangle]
.°. 360 - 2/_BOC = 180 - /_A
=> 180 = 2/_BOC - /_A
=> /_BOC = 90 + /_A/2
HENCE PROVED
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