Question 14
G5 (ARM) IMO5 Let $ABCDEF$ be a convex hexagon such that $AB$ is parallel to $DE$, $BC$ is parallel to $EF$, and $CD$ is parallel to $AF$. Let $R_A,R_C,R_E$ be the circumradii of triangles $FAB,BCD,DEF$ respectively, and let $P$ denote the perimeter of the hexagon. Prove that
$$R_A+R_C+R_E\ge\frac P2.$$
$$R_A+R_C+R_E\ge\frac P2.$$