CMO 1979 Problem 1

Given: (i) $a$ , $b > 0$ ; (ii) $a$ , $A_1$ , $A_2$ , $b$ is an arithmetic progression; (iii) $a$ , $G_1$ , $G_2$ , $b$ is a geometric progression. Show that $$A_1 A_2 \ge G_1 G_2.$$