Squares

Algebra Level 3

\[\large \bigg(\frac{a}{a+2b}\bigg)^2+\bigg(\frac{b}{b+2c}\bigg)^2+\bigg(\frac{c}{c+2a}\bigg)^2\]

If \(a,b\) and \(c\) are positive reals, find the minimum value of the expression above to 2 decimal places.