Para-Hexagon Concurrency Theorem

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.

Please enable Java for an interactive construction (with Cinderella).

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

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

Download an article of mine from the Mathematical Gazette (2006) for a proof of the result above from More on Hexagons with Opposite Sides Parallel


Created by Michael de Villiers, 6 June 2009 with Cinderella