In triangle ABC, the orthocenter O and the incenter I. If ∠BIC - ∠BOC = 90°, what is ∠A?
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Correct answer: D
Explanation
Given:
In triangle ABC, incenter = I
orthocenter = O
∠BIC − ∠BOC = 90°
By the formula:
∠BIC = 90° + A/2
∠BOC = 180° − A
(90° + A/2) − (180° − A) = 90°
90 + A/2 − 180 + A = 90
−90 + 3A/2 = 90
3A/2 = 180
A = 120°