Multiple choice

If S is the circumcentre of a triangle ABC and $\angle SAB=\angle SBC=\angle SCA=\theta$, then $\sin\theta=$

  1. 1
  2. $\displaystyle \frac{1}{2}$
  3. $\displaystyle \frac{1}{\sqrt{2}}$
  4. $\displaystyle \frac{\sqrt{3}}{2}$
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B Correct answer
Explanation

In a triangle where the circumcentre S satisfies the given angle conditions, the triangle must be equilateral. For an equilateral triangle, the circumcentre coincides with the centroid, and the angles SAB, SBC, and SCA are each 30 degrees. Since sin(30 degrees) = 1/2, the result follows.

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