The orthic axis of the excentral triangle, which is central line 
(Casey 1888, p. 177; Kimberling 1998, p. 150)
and therefore has trilinear equation
 |
It is the trilinear polar of the incenter.
The line passes through Kimberling centers 
for 
, 513, 649, 650, 652, 654, 656, 657, 659, 661, 672, 770,
798, 822, 851, 896, 899, 910, 1155, 1491, 1575, 1635, 1755, 2173, 2182, 2183, 2225,
2227, 2228, 2229, 2230, 2231, 2232, 2233, 2234, 2235, 2236, 2237, 2238, 2239, 2240,
2243, 2244, 2245, 2246, 2247, 2252, 2253, 2254, 2265, 2272, 2290, 2312, 2313, 2314,
2315, 2348, 2483, 2484, 2503, 2511, 2515, 2516, 2522, 2526, 2578, 2579, 2590, 2591,
2600, 2610, 2624, 2630, 2631, 2635, 2637, 2641, 2642, 3000, and 3013.
Amazingly, the antiorthic axis is the perspectrix of all pairwise combinations of the excentral triangle, extangents triangle, Feuerbach triangle, and reference triangle (Weisstein, Dec. 6. 2004).
The antiorthic axis is the radical line of the coaxal systems (Apollonius circle, excircles radical circle, nine-point circle) and (Bevan circle, circumcircle).
