1995 IMO Problems/Problem 5

Problem

Let $ABCDEF$ be a convex hexagon with $AB=BC=CD$ and $DE=EF=FA$ , such that $\angle BCD=\angle EFA=\frac{\pi}{3}$ . Suppose $G$ and $H$ are points in the interior of the hexagon such that $\angle AGB=\angle DHE=\frac{2\pi}{3}$ . Prove that $AG+GB+GH+DH+HE\ge CF$ .

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1995 IMO Problems/Problem 5

Problem

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