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IKMC 2027 - Grades 11-12 - Self-study SET 3 - Thematic Batch 3 Question 14

IKMC · IKMC 2027 - Grades 11-12 - Self-study SET 3 - Thematic Batch 3

Question 14

The six circles in the large square have radius 1. Two circles each touch three others; each of the remaining four touches one other circle, and their centres form a square. What is the area of the grey square?

Question illustration
  1. 2 + 8$\sqrt{2}$
  2. 4 + 5$\sqrt{3}$
  3. 5 + 4$\sqrt{5}$
  4. 6 + 3$\sqrt{6}$
  5. 8 + 2$\sqrt{7}$