The center of the Taylor circle. It has triangle center function α_389 = cos A - cos(2A) cos(B - C) and is Kimberling center X_389, which is the center of the Spieker circle of the orthic triangle of the reference triangle. The Taylor center lies on the Brocard axis. For an acute triangle Δ A B C, the Taylor center of Δ A B C is the Spieker center of the orthic triangle Δ H_A H_B H_C.

altitude | orthic triangle | Spieker center | Taylor circle

Brook Taylor