Combination of radii in triangle

Geometry Level 2

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 $R$ .

4{ R }^{ 2 }

16{ R }^{ 2 }

8{ R }^{ 2 }

2{ R }^{ 2 }

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