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X₁₀₆₇¶

ISOGONAL CONJUGATE OF X₁₀₆₆

X₁₀₆₇ is the isogonal conjugate of X₁₀₆₆.

X₁₀₆₇ (ISOGONAL CONJUGATE OF X₁₀₆₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1067 = ISOGONAL CONJUGATE OF X_1066."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            isogonal_conjugate,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01067(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1067 = ISOGONAL CONJUGATE OF X_1066 on reference triangle ABC."""
            X_1066 = eval_trilinear_point(model, A, B, C, '(1 - cos(A)*(cos(B) + cos(C)))', ID="X_1066", classes=["center"])
            X_1067 = isogonal_conjugate(model, A, B, C, X_1066, ID="X_1067", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_496 = eval_trilinear_point(model, A, B, C, '2 - cos(B - C)', ID="X_496", classes=["center", "incident"])
            central_line(model, X_3, X_496, 3, 496, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_1037 = eval_trilinear_point(model, A, B, C, '(1/(1 - cos(B)*cos(C)))', ID="X_1037", classes=["center", "incident"])
            central_line(model, X_4, X_1037, 4, 1037, incident=True)
            X_388 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2) + (b + c)**(2))/(b + c - a)', ID="X_388", classes=["center", "incident"])
            X_1059 = eval_trilinear_point(model, A, B, C, '(1/(2 - cos(B)*cos(C)))', ID="X_1059", classes=["center", "incident"])
            central_line(model, X_388, X_1059, 388, 1059, incident=True)
            return promote_point_to_top(model, X_1067)


        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_1067 on the given reference triangle."""
            model = create_model('X_1067 = ISOGONAL CONJUGATE OF X_1066')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01067(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-01067.json"))
            write_center_svg(
                model_acute,
                here / "x-01067.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1067¶

X₁₀₆₇¶