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MathNet 2004 — Part 02 Question 57

Math Olympiad Vault · MathNet 2004 — Part 02

Question 57

Calculate the area of the intersection of three circles having as their respective diameters the three sides of an equilateral triangle of unit side.
  1. $\frac{\sqrt{3}-\sqrt{2}}{3}$
  2. $\frac{\pi-3}{2}$
  3. $\pi-3$
  4. $\frac{\pi-\sqrt{3}}{4}$
  5. $\frac{\pi-\sqrt{3}}{8}$.