Geometry and inequality

Geometry Level 2

Let a,b,c be the lengths of the sides BC, CA, AB respectively of triangle ABC, and h be the altitude to the side BC. If for any triangle ABC, ( b + c ) 2 (b+c)^{2} a 2 a^{2} + λ h 2 h^{2} , then find the maximum value of λ .


The answer is 4.

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