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. Instead of the midpoints, one may take any other ratio t with P_23 M_23 :M_23 P_23^, = P_13 M_13 :M_13 P_13^, = P_12 M_12 :M_12 P_12^, = t and the points M_23, M_13, and M_12 will still be collinear in addition to bing tangent to the same parabola (Ehrmann and van Lamoen 2004).
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