Let \(ABC\) be a triangle with in-radius \(r\). Let \({ \Gamma }_{ 1 }, { \Gamma }_{ 2 }, { \Gamma }_{ 3 }\) be three circles inscribed inside \(ABC\) such that each touches other circles and also two of the sides. (Such a configuration is called Malfatti circles).

Let \({ O }_{ 1 }, { O }_{ 2 }, { O }_{ 3 }\) be respectively the centres of the circles \({ \Gamma }_{ 1 }, { \Gamma }_{ 2 }, { \Gamma }_{ 3 }\). If \(r'\) denotes the in-radius of \({ O }_{ 1 }{ O }_{ 2 }{ O }_{ 3 }\),

Find the minimum value of \( \frac r{r'}\) to 3 decimal places.

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