Question 36
Prove the inequality for positive $a$, $b$, $c$, $d$:
$$
\left(\frac{a+b}{2c}\right)^2 + \left(\frac{b+c}{2d}\right)^2 + \left(\frac{c+d}{2a}\right)^2 + \left(\frac{d+a}{2b}\right)^2 \ge 4.
$$
$$
\left(\frac{a+b}{2c}\right)^2 + \left(\frac{b+c}{2d}\right)^2 + \left(\frac{c+d}{2a}\right)^2 + \left(\frac{d+a}{2b}\right)^2 \ge 4.
$$