Malfatti Circles!

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.