Let
be a convex hexagon such that
is parallel to
,
is parallel to
, and
is parallel to
. Let
denote the circumradii of triangles
, respectively, and let
denote the perimeter of the hexagon. Prove that
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Let $ABCDEF$ be a convex hexagon such that $AB$ is parallel to $DE$, $BC$ 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
$$R_{A} + R_{C} + R_{E}\geq \frac {P}{2}.$$
Školjka