Triangle inside circles

Geometry Level 5

Three circles touch one another externally. The tangents at their points of contact meet at a point whose distance from a point of contact is 4. Find the ratio of the product of the radii to the sum of radii of circles, if your answer is in the form of \(\dfrac{r}{R}\), where \(r\) and \(R\) are coprime positive integers, submit your as \(r+R\).

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