If the midpoints of the opposite sides of a hexagon with opposite sides parallel are connected, then the three lines are concurrent at the centre of the conic circumscribed around the original hexagon.

Parallel-Hexagon Concurrency Theorem

1) Drag A, B, C, D or E - also check when ABCDEF becomes a crossed hexagon.

2) Can you explain why (prove) the above result is true?

3) Drag the vertices in pairs so that B and C, D and E, and A and F coincide, so that ABCDEF becomes a triangle (a degenerate hexagon). As shown below, this shows that the concurrency of the medians of a triangle is merely a special case of this more general theorem.