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X(2), X(11055)

Ga, Gb, Gc (antimedial triangle)

vertices of the cevian triangle of X(11055)

K371 is the unique isotomic pK which meets the Steiner ellipse at A, B, C and three other points forming an equilateral triangle T.

Its pivot is X(11055), the homothetic of X(76) under h(G,-3).

T has center X(7757), the reflection of X(76) in G. Its circumcircle passes through X(671), the antipode of the Steiner point X(99) in the Steiner ellipse. Its circum-radius is 4R sin^2 W, where W is the Brocard angle.

This triangle T is homothetic of the circumnormal triangle (vertices on the McCay cubic) at the point S = a^2(5b^2+5c^2-3a^2)-b^2c^2: : . It is also the reflection in G of the triangle formed by the isotomic conjugates of the infinite points of the sidelines of the Morley triangle. See "A Morley Configuration" in the Downloads page.

Compare K371 and K089, an isotomic nK whose root is X(11055) which also meets the Steiner ellipse at the vertices of an equilateral triangle.