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X₂₈₅₃¶

ISOGONAL CONJUGATE OF X₂₇₆₉

X₂₈₅₃ is the isogonal conjugate of X₂₇₆₉.

X₂₈₅₃ (ISOGONAL CONJUGATE OF X₂₇₆₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2853 = ISOGONAL CONJUGATE OF X_2769."""

        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_02853(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2853 = ISOGONAL CONJUGATE OF X_2769 on reference triangle ABC."""
            X_2769 = point_from_barycentrics(model, A, B, C, -0.088240128, 0.15600913, 0.932231, ID="X_2769", classes=["center"])
            X_2853 = isogonal_conjugate(model, A, B, C, X_2769, ID="X_2853", classes=["selected", "target"])
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", classes=["center", "incident"])
            X_112 = eval_trilinear_point(model, A, B, C, 'a/(sin(2*B) - sin(2*C))', ID="X_112", classes=["center", "incident"])
            central_line(model, X_109, X_112, 109, 112, incident=True)
            X_117 = point_from_barycentrics(model, A, B, C, 0.19223485, -0.017045455, 0.82481061, ID="X_117", classes=["center", "incident"])
            X_132 = point_from_barycentrics(model, A, B, C, 0.11002416, 0.049913231, 0.84006261, ID="X_132", classes=["center", "incident"])
            central_line(model, X_117, X_132, 117, 132, incident=True)
            X_124 = eval_trilinear_point(model, A, B, C, '(b*c*(b + c - a)*(b - c)**(2)*((b + c)*(b**(2) + c**(2) - a**(2) - b*c) + a*b*c))', ID="X_124", classes=["center", "incident"])
            X_127 = eval_trilinear_point(model, A, B, C, 'b*c*(sin(2*B) - sin(2*C))*((b**(2) - c**(2))*sin(2*A) - b**(2)*sin(2*B) + c**(2)*sin(2*C))', ID="X_127", classes=["center", "incident"])
            central_line(model, X_124, X_127, 124, 127, incident=True)
            return promote_point_to_top(model, X_2853)


        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_2853 on the given reference triangle."""
            model = create_model('X_2853 = ISOGONAL CONJUGATE OF X_2769')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02853(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-02853.json"))
            write_center_svg(
                model_acute,
                here / "x-02853.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2853¶

X₂₈₅₃¶