second isogonic center

The second Fermat point X' or F_2 (also known as the second isogonic center) can be constructed by drawing equilateral triangles on the inside of a given triangle and connecting opposite vertices. The three diagonals in the figure then intersect in the second Fermat point, which has triangle center function α = csc(A - 1/3 π) and is Kimberling center X_14. It also arises in Napoleon's theorem.

Fermat axis | Fermat points | first Fermat point | Napoleon's theorem