The figure below shows a quadrilateral ABCD
with E,F,G,H midpoints of the sides AB,BC,CD,AD. If M and N are the
midpoints of the diagonals AC and BD, prove that (1) EG,FH,MN are
concurrent at O, (2) O is the midpoint of EG,FH,MN.
Bimedian is a line segment that joins the midpoints of opposite sides of a quadrilateral
like EG and FH.