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X₂₀₄₅¶

5th EULER-VECTEN-GIBERT POINT

X₂₀₄₅ = inverse-in-orthocentroidal-circle of X₂₀₄₆

X₂₀₄₅ (5th EULER-VECTEN-GIBERT POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2045 = 5th EULER-VECTEN-GIBERT POINT."""

        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,
            centroid_of,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02045(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2045 = 5th EULER-VECTEN-GIBERT POINT on reference triangle ABC."""
            X_2045 = eval_trilinear_point(model, A, B, C, '(b*c*(- 2*(b**(2) - c**(2))**(2) + a**(2)*(3*b**(2) + 3*c**(2) - a**(2)) + 3**(1/2)*((b**(2) - c**(2))**(2) - a**(2)*(b**(2) + c**(2)))))', ID="X_2045", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_17 = eval_trilinear_point(model, A, B, C, 'csc(A +  pi  /6)', ID="X_17", classes=["center", "incident"])
            X_485 = eval_trilinear_point(model, A, B, C, 'sec(A -  pi  /4)', ID="X_485", classes=["center", "incident"])
            central_line(model, X_17, X_485, 17, 485, incident=True)
            X_18 = eval_trilinear_point(model, A, B, C, 'csc(A -  pi  /6)', ID="X_18", classes=["center", "incident"])
            X_486 = eval_trilinear_point(model, A, B, C, 'sec(A +  pi  /4)', ID="X_486", classes=["center", "incident"])
            central_line(model, X_18, X_486, 18, 486, incident=True)
            return promote_point_to_top(model, X_2045)


        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_2045 on the given reference triangle."""
            model = create_model('X_2045 = 5th EULER-VECTEN-GIBERT POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02045(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-02045.json"))
            write_center_svg(
                model_acute,
                here / "x-02045.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2045¶

X₂₀₄₅¶