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In a triangle ABC the bisectors of angle B and angle C intersect each other at a point O. prove that angle BOC= 90__ + half angle a__

2
__+ half angle a__

by aroravictor3

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by aroravictor3

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As we know A + B + C = 180

So, B + C = 180 - A

Or,

Now think in triangle BOC,

we have three angles, OBC, BOC and OCB

Let

So, X + (B/2) + (C/2) = 180

From equation (1)

b/2 + c/2 = 180 - a/2 - 1....

obc = b/2

ocb = c/2

boc =x

X + b/2 + c/2 = 180

x+ 180 - a/2 = 180

x = 90 + boc