Multiple choice

In a ∆ABC sides AB and AC extended to the point D and E respectively and the angle bisector of ∠CBD and ∠BCE meet at point O, if ∠ BAC = 80° then find ∠COB?

  1. 50°

  2. 40°

  3. 30°

  4. 60°
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A Correct answer
Explanation

In triangle ABC with external bisectors meeting at O: ∠COB = 90° - ∠A/2. Given ∠A = 80°, we get ∠COB = 90° - 40° = 50°. This is a standard result for the excenter opposite vertex A. The bisectors of external angles at B and C meet at the excenter.

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