A geometry problem by Aly Ahmed

Geometry Level 3

Let a , b , c a,b,c be the sides of a triangle. Find the maximum possible value of the expression below. a 2 + b 2 + c 2 a b + b c + c a + 3 ⋅ a b + b c + c a a 2 + b 2 + c 2 \dfrac{a^2+b^2+c^2}{ab + bc+ ca} + 3\cdot \dfrac{ab+bc+ca}{a^2+b^2+c^2}


The answer is 4.

Aly Ahmed by Aly Ahmed , 34, Egypt

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