New posts in Tangent Line Method

Prove that $\sum \limits_{cyc}\frac {a}{(b+c)^2} \geq \frac {9}{4(a+b+c)}$

Prove that, for any positive integer n: $(a + b)^{n} \leq 2^{n-1}(a^{n}+b^{n})$

Prove $\sqrt{a} + \sqrt{b} + \sqrt{c} \ge ab + bc + ca$

A inequality proposed at Zhautykov Olympiad 2008