Multiple choice

In a triangle ABC, O is its circumcentre and ∠BAC = 500.The measure of ∠OBC is.

  1. 300

  2. 400

  3. 500

  4. 600
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B Correct answer
Explanation

In any triangle, the angle at the center (circumcentre) is twice the angle at the circumference subtended by the same arc. Given ∠BAC = 50°, the central angle ∠BOC = 2 × 50° = 100°. Since O is the circumcentre, OB = OC (both are radii), so triangle OBC is isosceles. Therefore, ∠OBC = (180° - 100°)/2 = 40°. This uses the central angle theorem and properties of isosceles triangles.

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