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X₂₇₈₁¶

ISOGONAL CONJUGATE OF X₂₆₉₇

As the isogonal conjugate of a point on the circumcircle, X₂₇₈₁ lies on the line at infinity.

X₂₇₈₁ (ISOGONAL CONJUGATE OF X₂₆₉₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2781 = ISOGONAL CONJUGATE OF X_2697."""

        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,
            orthocenter_of,
            point_from_barycentrics,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02781(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2781 = ISOGONAL CONJUGATE OF X_2697 on reference triangle ABC."""
            X_2697 = point_from_barycentrics(model, A, B, C, 1.014769, 0.4666646, -0.48143363, ID="X_2697", classes=["center"])
            X_2781 = isogonal_conjugate(model, A, B, C, X_2697, ID="X_2781", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_67 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(4) + c**(4) - a**(4) - b**(2)*c**(2))', ID="X_67", classes=["center", "incident"])
            central_line(model, X_4, X_67, 4, 67, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            central_line(model, X_6, X_74, 6, 74, incident=True)
            X_22 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) - a**(4))', ID="X_22", classes=["center", "incident"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_22, X_110, 22, 110, incident=True)
            return promote_point_to_top(model, X_2781)


        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_2781 on the given reference triangle."""
            model = create_model('X_2781 = ISOGONAL CONJUGATE OF X_2697')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02781(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-02781.json"))
            write_center_svg(
                model_acute,
                here / "x-02781.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2781¶

X₂₇₈₁¶