[1] The isotomic image of the circumcircle is the orthic axis L of the anticomplementary A'B'C' of ABC. This line coincides with the trilinear polar of X

[2] This line is orthogonal to the Euler line and passes through X

[3] The isotomic conjugate of the line at infinity is the outer Steiner ellipse of the triangle.

[4] The isotomic conjugate of a line L is an (ellipse/parabola/hyperbola) if and only if the number of intersection points of L with the Steiner outer ellipse is (0/1/2).

[5] The isotomic conjugate of the X

[1] That the circumcircle is the isotomic image of the trilinear polar of X

To show [3] use the standard projectivity F mapping the equilateral triangle t

In the case of the equilateral triangle t

[4] Is a consequence of [3] and [5] is a standard calculation in trilinears. Note in this respect that the symmedian point K' of the anticomplementary is X

[1] That the circumcircle is the isotomic image of the trilinear polar of X

To show [3] use the standard projectivity F mapping the equilateral triangle t

[3] The isotomic conjugate of the line at infinity is the outer Steiner ellipse of the triangle.

[4] The isotomic conjugate of a line L is an (ellipse/parabola/hyperbola) if and only if the number of intersection points of L with the Steiner outer ellipse is (0/1/2).

[5] The isotomic conjugate of the X

IsotomicChart.html

IsotomicConicOfLine.html

IsotomicGeneral.html

Steiner_Ellipse.html

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