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IKMC 2007 - Grades 9-10 - Self-study Question 23

IKMC · IKMC 2007 - Grades 9-10 - Self-study

Question 23

An equilateral triangle and regular hexagon are inscribed in a circle, which is inscribed in a larger equilateral triangle. Areas are S 1 (large triangle), S 2 (small triangle), S 3 (hexagon). Which relation holds?

Question illustration
  1. $S_3=\sqrt{S_1S_2}$
  2. $S_3=S_1S_2/2$
  3. $S_1=S_2+S_3$
  4. $S_3=\sqrt{S_1^2S_2^2}$
  5. $S_1=S_3+3S_2$