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Two circles, both of radii $1$ cm, intersect such that the circumference of each one passes through the centre of the other. What is the area (in sq cm) of the intersecting region?

  1. $\frac{\pi}{3} - \frac{\sqrt{3}} {4} $
  2. $\frac{2 \pi}{3} + \frac{\sqrt{3}} {2} $
  3. $\frac{4 \pi}{3} - \frac{\sqrt{3}} {2} $
  4. $\frac{4 \pi}{3} + \frac{\sqrt{3}} {2} $
  5. $\frac{2 \pi}{3} - \frac{\sqrt{3}} {2} $
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