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# Antiorthic Axis

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).

Central Line, Coaxal System, Orthic Axis

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## References

Casey, J. A Sequel to the First Six Books of the Elements of Euclid, Containing an Easy Introduction to Modern Geometry with Numerous Examples, 5th ed., rev. enl. Dublin: Hodges, Figgis, & Co., 1888.Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.

Antiorthic Axis

## Cite this as:

Weisstein, Eric W. "Antiorthic Axis." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AntiorthicAxis.html