← etc / Encyclopedia of Triangle Centers

X₉₁₈¶

ISOTOMIC CONJUGATE OF X₆₆₆

As the isogonal conjugate of a point of the circumcircle, X₉₁₈ lies on the line at infinity.

X₉₁₈ (ISOTOMIC CONJUGATE OF X₆₆₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_918 = ISOTOMIC CONJUGATE OF X_666."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00918(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_918 = ISOTOMIC CONJUGATE OF X_666 on reference triangle ABC."""
            X_918 = eval_barycentric_point(model, A, B, C, '((b - c)*(b**(2) + c**(2) -a*b - a*c))', ID="X_918", classes=["selected", "target"])
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            central_line(model, X_30, X_511, 30, 511, incident=True)
            X_63 = eval_trilinear_point(model, A, B, C, 'cot(A)', ID="X_63", classes=["center", "incident"])
            X_654 = eval_trilinear_point(model, A, B, C, 'cos(A - B) - cos(C - A)', ID="X_654", classes=["center", "incident"])
            central_line(model, X_63, X_654, 63, 654, incident=True)
            X_190 = eval_trilinear_point(model, A, B, C, 'b*c/(b - c)', ID="X_190", classes=["center", "incident"])
            X_644 = eval_trilinear_point(model, A, B, C, '((b + c - a)/(b - c))', ID="X_644", classes=["center", "incident"])
            central_line(model, X_190, X_644, 190, 644, incident=True)
            return promote_point_to_top(model, X_918)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_918 on the given reference triangle."""
            model = create_model('X_918 = ISOTOMIC CONJUGATE OF X_666')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00918(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-00918.json"))
            write_center_svg(
                model_acute,
                here / "x-00918.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X918¶

X₉₁₈¶