The Nine-Point Circle and the Euler Line
The pedal circle of H and O is the nine-point circle of the triangle. The center of the circle is the midpoint of H and O, N.
The centroid G lies on the line.
The deLonchamps point, which is the reflection of H in O, lies on the line.
The ratios along this line are HN:NG:GO:OL = 3:1:2:6.