Combination of radii in triangle

Geometry Level pending

In a triangle \(ABC\), we define \(r\) as the inradius, \(r_A, r_B, r_C\) as the exradii of sides \(a,b,c\) respectively and \(R\) as its circumradius.

Express \(r^2 + r_A^2 + r_B^2 + r_C^2 + a^2 + b^2 + c^2 \) in terms of \(R\).

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