A geometry problem by Anish Roy

Geometry Level 5

\[ \frac{ a^2 + 2bc } { b^2 + c^2 } + \frac{ b^2 + 2ca } { c^2 + a^2 } + \frac{ c^2 + 2ab } { a^2 + b^2 } \] Given that \( a, b , c \) are the side lengths of a triangle, what is the infimum value of the expression above?

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