If in a triangle ABC the external bisector of angle ABC and angle ACB meet at O then proof that angle BOC =90degree -1/2 angle BAC
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Since bd is perpendicular it forms triangle abd with half angle b that is 45 degree
then consider triangle bdc we have at b as 45 degrees and d as 90 degree then by angle sum property of triangle
we have
90+45+angle c=180
135+c=180
c=180-135=45 degrees
hence angle abd =angle acb
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