Geometry · Convex hexagon · Parallel lines · Areas of triangles
In a convex hexagon \(ABCDEF\) the following lines are parallel:
\[ AB \parallel FC \parallel DE, \qquad BC \parallel AD \parallel EF, \qquad CD \parallel BE. \]
Prove that \(BE \parallel FA\).
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Serbian Municipal Competition 2015, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source