Question

bisector of Angle B and C of a triangle ABC intersect each other at the point O . prove that angle BOC = 90 + half angleA​

Answer 1

Explanation:

in triangle ABC

angle A + angle B + angle C = 180

( dividing whole equation by 2 )

A/2 + B/2 + C /2 = 90

B/2 + C /2 = 90 - A/2

let this equatiin be 1

in triangle BOC

as the line bisects angle B the angle inside triangle BOC is B/2

as the line bisects angle C the angle inside triangle BOC is C/2

so in triangle BOC

B/2 + C/2 + angle BOC = 180

( from equation 1..... substitution in this equation)

90 - A/2 + angle BOC = 180

angle BOC = 180 - 90 - A/2

angle BOC = 90 - A/2

Answer 2

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