Droz-Farny line theorem

If two perpendicular lines are drawn through the orthocenter H of any triangle, these lines intercept each side (or its extension) in two points (labeled P_12, P_12^, , P_13, P_13^, , P_23, P_23^, ). Then the midpoints M_12, M_12, and M_23 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.

collinear | midpoint