Question

In the figure BO and CO are angle bisectors show that angle BOC =90+ 1/2 angle A

Answer 1

Answer:

BO and CO are angle bisector of angle B and angle C respectively

Then,

Angle B = angle OBC + angle OBA

(where angle OBC = angle OBA)

Then,

Angle B = 2 angle OBC

Angle C = angle OCB + angle OCA

(where angle OCB = angle OCA)

Then,

Angle C = 2 angle OCB

In triangle ABC,

Angle A + angle B + angle C = 180

Angle A + 2 angle OBC + 2 angle OCB = 180

2(angle OBC + angle OCB) =180 - angle A

Angle OBC + angle OCB = (180 - angle A) /2

Angle OBC + angle OCB = 90 - 1/2 angle A

In triangle BOC,

Angle OBC + angle OCB + angle BOC = 180

90 - 1/2 angle A + angle BOC = 180

Angle BOC = 180 - 90 + 1/2 angle A

Angle BOC = 90 + 1/2 angle A

Hence proved