InterviewSolution
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InterviewSolution
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in the triangle ABC the bisector of Angle B and angle C intersect each other at point O prove that angle BOC barabar 90 degree 1upon 2 < A |
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Answer» Ray BO is the bisector of angle CBE Therefore,angle CBO=1/2of angle CBE=1/2(180-y)=90-y/2 (1)Similarly,ray OC is the bisector of angle BCD Therefore,angle BCO=1/2 of angle BCD=1/2(180-z)=90-z/2 (2)In triangle BOC,angle BOC+BCO+CBO=180 (3)Substituting (1,2,3) you getAngle BOC+90-z/2+90-y/2=180Angle BOC=z/2+y/2=1/2(y+z)But,x+y+z=180 (angle sum property)y+z=180-xAngle BOC=1/2(180-x)=90-x/2=90-1/2angle BAC |
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