Let 
be a quadrilateral with perpendicular polygon diagonals. The midpoints
of the sides (
,
,
,
and 
)
determine a parallelogram (the Varignon
parallelogram) with sides parallel to the polygon
diagonals. The eight-point circle passes through the four midpoints
and the four feet of the perpendiculars from the
opposite sides 
, 
, 
, and 
.
