Maximum obtuse

Geometry Level pending

In the plane are given a triangle and three circles tangent to triangle  and externally tangent to each other. The triangle formed by the centers of the circles is obtuse, then find the maximum obtuse angle of the triangle that can be formed can be written in the form of :

\(a\sin^{-1}\left(\frac{b}{c}\right)\).

Evaluate \(a+b+c\)

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