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X₂₉₇₀¶

4th MACBEATH POINT

X₂₉₇₀ (4th MACBEATH POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2970 = 4th MACBEATH 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,
            ceva_conjugate,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02970(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2970 = 4th MACBEATH POINT on reference triangle ABC."""
            X_847 = eval_trilinear_point(model, A, B, C, 'sec(A)*sec(2*A)', ID="X_847", classes=["center"])
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center"])
            X_2970 = ceva_conjugate(model, A, B, C, X_847, X_523, ID="X_2970", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_94 = eval_trilinear_point(model, A, B, C, 'csc(3*A)', ID="X_94", classes=["center", "incident"])
            central_line(model, X_4, X_94, 4, 94, incident=True)
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            central_line(model, X_25, X_98, 25, 98, 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_135 = eval_trilinear_point(model, A, B, C, '(sec(A))*((sin(2*B))/(sec(2*C) - sec(2*A)) + (sin(2*C))/(sec(2*A) - sec(2*B)))', ID="X_135", classes=["center", "incident"])
            central_line(model, X_115, X_135, 115, 135, incident=True)
            return promote_point_to_top(model, X_2970)


        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_2970 on the given reference triangle."""
            model = create_model('X_2970 = 4th MACBEATH POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02970(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-02970.json"))
            write_center_svg(
                model_acute,
                here / "x-02970.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2970¶

X₂₉₇₀¶