van Aubel Line

The van Aubel line is the line in the plane of a reference triangle that connects the orthocenter and symmedian point , and symmedian point of the orthic triangle. The collinearity of these three points is given as an exercise and ascribed to van Aubel by Casey (1888, Exercise 77, p. 241).

The van Aubel line is central line , and has trilinear equation

which can also be written as

(P. Moses, pers. comm., Mar. 24, 2005).

A complete list of Kimberling centers through which it passes is given by (orthocenter ), 6 (symmedian point ), 53 (symmedian point of the orthic triangle), 217, 387, 393, 397, 398, 1172, 1181, 1199, 1249, 1498, 1503, 1514, 1515, 1540, 1547, 1548, 1549, 1587, 1588, 1834, 1865, 1901, 1990, 2207, 2211, 2442, and 2883.

It is perpendicular to lines (3,878), (30,511), (99,249), (110,935), (297,850), (323,401), and (441,647). It is parallel to lines (2,154), (3,66), (4,6), (5,182), (11,1428), (20,64), (22,161), (30,511), (51,428), (67,74), (98,230), (110,858), (125,468), (147,325), (184,427), (221,388), (242,1146), (265,1177), (287,297), (376,599), (381,597), (382,1351), (383,395), (394,1370), (396,1080), (546,575), (576,1353), (611,1478), (613,1479), and (946,1386).

The trilinear pole of the line is Kimberling center .