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X₆₆₈¶

TRILINEAR POLE OF LINE X₂X_37

As the trilinear product of Steiner circumellipse antipodes, X₆₆₈ lies on conic {A, B, C,X₆₆₈,X₇₈₉}} with center X₆₃₇₆ and perspector X₇₅. (Randy Hutson, July 11, 2019)

X₆₆₈ (TRILINEAR POLE OF LINE X₂X_37) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_668 = TRILINEAR POLE OF LINE X_2X_37."""

        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_trilinear_point,
            isogonal_conjugate,
            nagel_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00668(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_668 = TRILINEAR POLE OF LINE X_2X_37 on reference triangle ABC."""
            X_667 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b - c)', ID="X_667", classes=["center"])
            X_668 = isogonal_conjugate(model, A, B, C, X_667, ID="X_668", classes=["selected", "target"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            central_line(model, X_8, X_76, 8, 76, incident=True)
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center", "incident"])
            central_line(model, X_99, X_100, 99, 100, incident=True)
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            X_150 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(4) + c**(4) - a**(4) + a*(b*c**(2) +c*b**(2) - b**(3) - c**(3)) - b*c*(a**(2) + b**(2) + c**(2)) + (b + c)*a**(3)))', ID="X_150", classes=["center", "incident"])
            central_line(model, X_69, X_150, 69, 150, incident=True)
            return promote_point_to_top(model, X_668)


        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_668 on the given reference triangle."""
            model = create_model('X_668 = TRILINEAR POLE OF LINE X_2X_37')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00668(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-00668.json"))
            write_center_svg(
                model_acute,
                here / "x-00668.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X668¶

X₆₆₈¶