# 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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