The two large gray circles are congruent, and each is half the diameter of the largest circle. All circles that appear to be tangent to each other *are* indeed tangent to each other.

\[ \frac{\text{radius of blue circle}}{\text{radius of red circle}} = \frac{a}{b}, \]

where \(a\) and \(b\) are coprime positive integers. Find \(a+b\).

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