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Gaokao Math Practice Question

已知 $\triangle A B C$ 是面积为 $\frac{9 \sqrt{3}}{4}$ 的等边三角形, 且其顶点都在球 $O$ 的球面上. 若球 $O$ 的表面积为 $16 \pi$, 则 $O$ 到平面 $A B C$ 的距离为 ($\quad$)

  1. A.$\sqrt{3}$
  2. B.$\frac{3}{2}$
  3. C.1
  4. D.$\frac{\sqrt{3}}{2}$

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