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X₂₈₂₆¶

ISOGONAL CONJUGATE OF X₂₇₄₂

X₂₈₂₆ is the isogonal conjugate of X₂₇₄₂.

X₂₈₂₆ (ISOGONAL CONJUGATE OF X₂₇₄₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2826 = ISOGONAL CONJUGATE OF X_2742."""

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


        def construct_x_02826(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2826 = ISOGONAL CONJUGATE OF X_2742 on reference triangle ABC."""
            X_2742 = point_from_barycentrics(model, A, B, C, 0.20138889, 1.1116667, -0.31305556, ID="X_2742", classes=["center"])
            X_2826 = isogonal_conjugate(model, A, B, C, X_2742, ID="X_2826", classes=["selected", "target"])
            X_104 = eval_trilinear_point(model, A, B, C, '1/(-1 + cos(B) + cos(C))', ID="X_104", classes=["center", "incident"])
            X_105 = eval_trilinear_point(model, A, B, C, '1/(b**(2) + c**(2) - a*(b + c))', ID="X_105", classes=["center", "incident"])
            central_line(model, X_104, X_105, 104, 105, incident=True)
            X_119 = eval_trilinear_point(model, A, B, C, '(csc(A))*(-1 + cos(B) + cos(C))*(sin(2*B) + sin(2*C) + 2*(-1 + cos(A))*(sin(B) + sin(C)))', ID="X_119", classes=["center", "incident"])
            X_120 = eval_trilinear_point(model, A, B, C, 'b*c*(2*a*b*c - (b + c)*(a**(2) + (b - c)**(2)))*(b**(2) + c**(2) - a*b -a*c)', ID="X_120", classes=["center", "incident"])
            central_line(model, X_119, X_120, 119, 120, incident=True)
            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)
            return promote_point_to_top(model, X_2826)


        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_2826 on the given reference triangle."""
            model = create_model('X_2826 = ISOGONAL CONJUGATE OF X_2742')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02826(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-02826.json"))
            write_center_svg(
                model_acute,
                here / "x-02826.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2826¶

X₂₈₂₆¶