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X₂₈₀₈¶

ISOGONAL CONJUGATE OF X₂₇₂₄

X₂₈₀₈ is the isogonal conjugate of X₂₇₂₄.

X₂₈₀₈ (ISOGONAL CONJUGATE OF X₂₇₂₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2808 = ISOGONAL CONJUGATE OF X_2724."""

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


        def construct_x_02808(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2808 = ISOGONAL CONJUGATE OF X_2724 on reference triangle ABC."""
            X_2724 = point_from_barycentrics(model, A, B, C, 0.99050454, -0.024659864, 0.034155329, ID="X_2724", classes=["center"])
            X_2808 = isogonal_conjugate(model, A, B, C, X_2724, ID="X_2808", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            central_line(model, X_3, X_101, 3, 101, incident=True)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_116 = eval_trilinear_point(model, A, B, C, 'b*c*((b - c)**(2)*(b**(2) + b*c + c**(2) - a*b - a*c))', ID="X_116", classes=["center", "incident"])
            central_line(model, X_5, X_116, 5, 116, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", 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_4, X_150, 4, 150, incident=True)
            return promote_point_to_top(model, X_2808)


        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_2808 on the given reference triangle."""
            model = create_model('X_2808 = ISOGONAL CONJUGATE OF X_2724')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02808(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-02808.json"))
            write_center_svg(
                model_acute,
                here / "x-02808.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2808¶

X₂₈₀₈¶