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X₂₃₉₁¶

ISOGONAL CONJUGATE OF X₂₃₇₁

As the isogonal conjugate of a point on the circumcircle, X₂₃₉₁ lies on the line at infinity.

X₂₃₉₁ (ISOGONAL CONJUGATE OF X₂₃₇₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2391 = ISOGONAL CONJUGATE OF X_2371."""

        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_02391(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2391 = ISOGONAL CONJUGATE OF X_2371 on reference triangle ABC."""
            X_2371 = point_from_barycentrics(model, A, B, C, 0.63920015, 1.0190677, -0.65826781, ID="X_2371", classes=["center"])
            X_2391 = isogonal_conjugate(model, A, B, C, X_2371, ID="X_2391", classes=["selected", "target"])
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center", "incident"])
            X_279 = eval_trilinear_point(model, A, B, C, 'csc(A)*(tan(A/2))**(2)', ID="X_279", classes=["center", "incident"])
            central_line(model, X_57, X_279, 57, 279, 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)
            X_910 = point_from_barycentrics(model, A, B, C, -1.9642857, -1.2857143, 4.25, ID="X_910", classes=["center", "incident"])
            X_1323 = eval_trilinear_point(model, A, B, C, '(((sec(A/2))**(2))*(2*(cos(A/2))**(2) - (cos(B/2))**(2) - (cos(C/2))**(2)))', ID="X_1323", classes=["center", "incident"])
            central_line(model, X_910, X_1323, 910, 1323, incident=True)
            return promote_point_to_top(model, X_2391)


        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_2391 on the given reference triangle."""
            model = create_model('X_2391 = ISOGONAL CONJUGATE OF X_2371')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02391(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-02391.json"))
            write_center_svg(
                model_acute,
                here / "x-02391.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2391¶

X₂₃₉₁¶