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2025 AMC 10B Question 12

AMC10 · 2025 AMC 10B

Question 12

The figure below shows an equilateral triangle, a rhombus with a $60^\circ$ angle, and a regular hexagon, each of them containing some mutually tangent congruent disks. Let $T,$ $R,$ and $H,$ respectively, denote the ratio in each case of the total area of the disks to the area of the enclosing polygon.

Question illustration

Which of the following is true?
  1. $T = H = R$
  2. $H \lt R = T$
  3. $H = R \lt T$
  4. $H \lt R \lt T$
  5. $H \lt T \lt R$