English: 9-point circles (yellow) and circumcircles (violet) and green lines from the orange orthocenter. From the left obtuse triangle, right triangle, acute triangle and equilateral triangle. Euler line black.
O = orthocenter
N = nine-point center
E = circumcenter
To show that a green line from the orthocenter that intersects the circumcircle is divided in half by the 9-point circle. To the left obtuse triangle, to the ricght acute triangle. Euler line black. To show that a line from the orthocenter that intersects the circumcircle is divided in half by the 9-pt circle (as triangles ONA and ONB are scalable by a factor 2.