IR-TST 2018 Problem 2

Determine the least real number $k$ such that the inequality $$\left(\frac{2a}{a-b}\right)^2+\left(\frac{2b}{b-c}\right)^2+\left(\frac{2c}{c-a}\right)^2+k \geq 4\left(\frac{2a}{a-b}+\frac{2b}{b-c}+\frac{2c}{c-a}\right)$$ holds for all real numbers $a,b,c$ .

Proposed by Mohammad Jafari