Multiple choice

If O is the circumcentre of ΔABC and ∠OBC = 400, then the ∠BAC is equal to. यदि O, ΔABC का परिकेन्द्र है और ∠OBC = 400, तो ∠BAC है।

  1. 500

  2. 800

  3. 640

  4. 620
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A Correct answer
Explanation

If O is circumcenter of ΔABC, then O is equidistant from all vertices, so OA = OB = OC = R (circumradius). In ΔOBC, ∠OBC = 40° and OB = OC, so ∠OCB = 40°. Then ∠BOC = 180° - 2×40° = 100°. At circumcenter, central angle is twice inscribed angle: ∠BOC = 2∠BAC. So 100° = 2∠BAC, giving ∠BAC = 50°.

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