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AMC 10B 2025 (Problem 12)

The figure below shows an equilateral triangle, a rhombus with a 60∘60^\circ angle, and a regular hexagon, each of them containing some mutually tangent congruent disks. Let TT, RR, and HH, respectively, denote the ratio in each case of the total area of the disks to the area of the enclosing polygon. Which of the following is true?
An equilateral triangle, a rhombus, and a regular hexagon containing mutually tangent congruent disks
(A)  T=H=R\text{(A)}\;\text{T=H=R}(B)  H<R=T\text{(B)}\;\text{H<R=T}(C)  H=R<T\text{(C)}\;\text{H=R<T}(D)  H<R<T\text{(D)}\;\text{H<R<T}(E)  H<T<R\text{(E)}\;\text{H<T<R}