Question

Bisectors of Angle B and angle C of a triangle ABC intersect each other at the point O prove that angle BOC = 90 degree + half of angle A

Answer 1

Answer:

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Refer to the attachment...

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Answer 2

To prove angle BOC = 90°+1/2 angle a

Proof: In triangle ABC

angle a+ angle B + angle c = 180° ( by angle sum property)

angle a + 2angle OBC+ 2angle ocb =180°

2( angle OBC+ angle ocb) =180°-angle a

angle obc + angle ocb = 180°/2-angle a/2

angle obc + angle ocb = 90°- a/2

Now in triangle BOC

angle boc + angle obc + angle ocb = 180° ( by angle sum property)

angle boc = 180° - ( angle obc+ angle ocb)

angle boc = 180° - (90°-angle a/2)

angle boc = 180°-90°+angle a/2

angle boc = 90°+angle a/2

H.P.