If two perpendicular lines are drawn through the orthocenter of any triangle, these lines intercept
each side (or its extension) in two points (labeled , , , , , ). Then the midpoints, , and of these three segments are collinear.
The two given lines, the lines connecting the midpoints and the sides of the reference triangle are all tangent to the same (inscribed) parabola. Instead of the midpoints,
one may take any other ratio with
and the points ,
,
and
will still be collinear in addition to bing tangent to the same parabola (Ehrmann
and van Lamoen 2004).
of any triangle, these lines intercept
each side (or its extension) in two points (labeled 
, 
, 
, 
, 
, 
). Then the midpoints 
, 
, and 
of these three segments are collinear.
with
,
,
and 
will still be collinear in addition to bing tangent to the same parabola (Ehrmann
and van Lamoen 2004).
