In triangle abc, if external bisectors of the anlge b and c meet at the point 0. if angle a =70 degree
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I will be using A, B, C not angle A or angle B.... Hope you will not mind it.
As we know A + B + C = 180
So, B + C = 180 - A
Or, (B/2) + (C/2) = 90 - (A/2) ....(1)
Now think in triangle BOC,
we have three angles, OBC, BOC and OCB
OBC = (B/2)
OCB = (C/2)
Let BOC = X
So, X + (B/2) + (C/2) = 180
From equation (1)
X + 90 - (A/2) = 180
X = 90 + A/2 (Proved !!!)
As we know A + B + C = 180
So, B + C = 180 - A
Or, (B/2) + (C/2) = 90 - (A/2) ....(1)
Now think in triangle BOC,
we have three angles, OBC, BOC and OCB
OBC = (B/2)
OCB = (C/2)
Let BOC = X
So, X + (B/2) + (C/2) = 180
From equation (1)
X + 90 - (A/2) = 180
X = 90 + A/2 (Proved !!!)
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