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X₂₇₇₇¶

ISOGONAL CONJUGATE OF X₂₆₉₃

As the isogonal conjugate of a point on the circumcircle, X₂₇₇₇ lies on the line at infinity.

X₂₇₇₇ (ISOGONAL CONJUGATE OF X₂₆₉₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2777 = ISOGONAL CONJUGATE OF X_2693."""

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


        def construct_x_02777(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2777 = ISOGONAL CONJUGATE OF X_2693 on reference triangle ABC."""
            X_2693 = point_from_barycentrics(model, A, B, C, 0.99105015, 0.5476195, -0.53866965, ID="X_2693", classes=["center"])
            X_2777 = isogonal_conjugate(model, A, B, C, X_2693, ID="X_2777", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            central_line(model, X_4, X_74, 4, 74, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_113 = eval_trilinear_point(model, A, B, C, 'sin(B)*sin(C)*((sin(C))/(cos(C) - 2*cos(A)*cos(B)) + (sin(B))/(cos(B) - 2*cos(A)*cos(C)))', ID="X_113", classes=["center", "incident"])
            central_line(model, X_3, X_113, 3, 113, incident=True)
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center", "incident"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_20, X_110, 20, 110, incident=True)
            return promote_point_to_top(model, X_2777)


        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_2777 on the given reference triangle."""
            model = create_model('X_2777 = ISOGONAL CONJUGATE OF X_2693')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02777(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-02777.json"))
            write_center_svg(
                model_acute,
                here / "x-02777.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2777¶

X₂₇₇₇¶