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X₂₄₂₃¶

ISOGONAL CONJUGATE OF X₂₃₉₇

X₂₄₂₃ is the isogonal conjugate of X₂₃₉₇.

X₂₄₂₃ (ISOGONAL CONJUGATE OF X₂₃₉₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2423 = ISOGONAL CONJUGATE OF X_2397."""

        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,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02423(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2423 = ISOGONAL CONJUGATE OF X_2397 on reference triangle ABC."""
            X_2397 = point_from_barycentrics(model, A, B, C, -6, 1, 6, ID="X_2397", classes=["center"])
            X_2423 = isogonal_conjugate(model, A, B, C, X_2397, ID="X_2423", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_650 = eval_trilinear_point(model, A, B, C, 'cos(B) - cos(C)', ID="X_650", classes=["center", "incident"])
            central_line(model, X_6, X_650, 6, 650, incident=True)
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            X_663 = eval_trilinear_point(model, A, B, C, 'a*(b - c)*(b + c - a)', ID="X_663", classes=["center", "incident"])
            central_line(model, X_31, X_663, 31, 663, incident=True)
            X_104 = eval_trilinear_point(model, A, B, C, '1/(-1 + cos(B) + cos(C))', ID="X_104", classes=["center", "incident"])
            X_739 = eval_trilinear_point(model, A, B, C, '1/(a**(-2)*(b**(0) + c**(0)) - a **(-1)*(b **(-1) + c **(-1)))', ID="X_739", classes=["center", "incident"])
            central_line(model, X_104, X_739, 104, 739, incident=True)
            return promote_point_to_top(model, X_2423)


        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_2423 on the given reference triangle."""
            model = create_model('X_2423 = ISOGONAL CONJUGATE OF X_2397')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02423(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-02423.json"))
            write_center_svg(
                model_acute,
                here / "x-02423.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2423¶

X₂₄₂₃¶