The lines containing the bisectors of the exterior angles at vertices B and C of triangle ABC intersect at point O. find angle BOC if angle A is equal to alpha

Gavyn Whitehead 2022-09-12 Answered
The lines containing the bisectors of the exterior angles at vertices B and C of triangle ABC intersect at point O. find angle BOC if angle A is equal to α.
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Answers (1)

Aubrie Conley
Answered 2022-09-13 Author has 13 answers
In the triangle ABC, the interior angles are: A = a , B = x , C = 180 a x.
External corners: in B = 180 x and in C = a + x.
In a triangle BOC, by condition, the angles are equal:
O B C = i n B / 2 = ( 180 x ) / 2 = 90 x / 2 ;
O C B = i n C / 2 = ( a + x ) / 2 = a / 2 + x / 2.
Then B O C = 180 B O C O C B = 180 ( 90 x / 2 ) ( a / 2 + x / 2 ) = 90 a / 2
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