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X₂₀₂₈¶

1st BROCARD-AXIS-MOSES-CIRCLE INTERSECTION

Of the two points of intersection of the Brocard axis, X₃ X₆ with the Moses circle, X₂₀₂₈ is the one nearer to X₃. Points X₂₀₂₈ and X₂₀₂₉ are the points of intersection of the Brocard axis and the asymptotes of the Kiepert hyperbola; see X₂₀₃₉ and X₂₀₄₀. For a description of the Moses circle and others, see the notes just above X₁₆₆₂.

X₂₀₂₈ (1st BROCARD-AXIS-MOSES-CIRCLE INTERSECTION) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2028 = 1st BROCARD-AXIS-MOSES-CIRCLE INTERSECTION."""

        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,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02028(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2028 = 1st BROCARD-AXIS-MOSES-CIRCLE INTERSECTION on reference triangle ABC."""
            X_2028 = eval_trilinear_point(model, A, B, C, '(sin(A) - e*sin(A +  omega  ) - sin(A + 2*omega  ))', ID="X_2028", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_3, X_6, 3, 6, incident=True)
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            X_2039 = eval_trilinear_point(model, A, B, C, 'e*cos(A) + 2*e*cos(B)*cos(C) + cos(A +  omega  )', ID="X_2039", classes=["center", "incident"])
            central_line(model, X_115, X_2039, 115, 2039, incident=True)
            X_1506 = eval_trilinear_point(model, A, B, C, 'b*c*((b**(2) - c**(2))**(2) - 2*a**(2)*(b**(2) + c**(2)))', ID="X_1506", classes=["center", "incident"])
            X_2040 = eval_trilinear_point(model, A, B, C, 'e*cos(A) + 2*e*cos(B)*cos(C) - cos(A +  omega  )', ID="X_2040", classes=["center", "incident"])
            central_line(model, X_1506, X_2040, 1506, 2040, incident=True)
            return promote_point_to_top(model, X_2028)


        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_2028 on the given reference triangle."""
            model = create_model('X_2028 = 1st BROCARD-AXIS-MOSES-CIRCLE INTERSECTION')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02028(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-02028.json"))
            write_center_svg(
                model_acute,
                here / "x-02028.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2028¶

X₂₀₂₈¶