# Difference between revisions of "1995 IMO Problems/Problem 5"

Tigerzhang (talk | contribs) (Created page with "==Problem== Let <math>ABCDEF</math> be a convex hexagon with <math>AB=BC=CD</math> and <math>DE=EF=FA</math>, such that <math>\angle BCD=\angle EFA=\frac{\pi}{3}</math>. Suppo...") |
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==Problem== | ==Problem== | ||

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

+ | ==Solution== |

## Revision as of 20:04, 5 July 2020

## Problem

Let be a convex hexagon with and , such that . Suppose and are points in the interior of the hexagon such that . Prove that .