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The internal bisectors of ∠B and ∠C of triangle ABC meet at O, and ∠BOC is three times ∠A. Find ∠A.

Competition practiceGeometry

A36°
B30°
C45°
D54°

Step-by-Step Solution

For internal bisectors,

∠ BOC = 90° + \frac{∠ A}{2}

. So

90 + \frac{A}{2} = 3 A

, giving

2.5 A = 90

and

A = 36

°.

Answer: A) 36°

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