# 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?

×