1996 IMO Problems/Problem 5

Problem

Let $ABCDEF$ be a convex hexagon such that $AB$ is parallel to $DE$ , $BD$ is parallel to $EF$ , and $CD$ is parallel to $FA$ . Let $R_{A}$ , $R_{C}$ , $R_{E}$ denote the circumradii of triangles $FAB$ , $BCD$ , $DEF$ , respectively, and let $P$ denote the perimeter of the hexagon. Prove that

$R_{A}+R_{C}+R_{E} \ge \frac{P}{2}$

Solution

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1996 IMO Problems/Problem 5

Problem

Solution