MathNet 1998 — Part 01 Question 51

Let $a_i, b_i, c_i$ and $R_i$ ($i = 1, 2$) be the sides and the radii of the circumscribed circles of $\triangle A_iB_iC_i$. Prove that for $m, n \ge 1$, $a_1^m a_2^n + b_1^m b_2^n + c_1^m c_2^n \le 9(2^{m+n-2} R_1^m R_2^n)$.