Square ratios

Geometry Level 3

The blue square touches each side of the largest square, filling \(\frac{29}{50}\) of it.

Each of the 4 red squares at the corners of the largest square touch the blue square.

The fraction of the largest square that is red is \(\frac{a}{b},\) where \(a\) and \(b\) are positive coprime integers.

What is \(a+b?\)

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