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X₂₉₇₃¶

7th MACBEATH POINT

X₂₉₇₃ = cevapoint of X₁₉₈₆ and X₂₉₆₉

X₂₉₇₃ (7th MACBEATH POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2973 = 7th 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,
            cevapoint,
            circumcenter_of,
            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_02973(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2973 = 7th MACBEATH POINT on reference triangle ABC."""
            X_1986 = eval_trilinear_point(model, A, B, C, '(1 + cos(2*B) + cos(2*C))*sin(3*A)*csc(2*A)', ID="X_1986", classes=["center"])
            X_2969 = eval_trilinear_point(model, A, B, C, '((b - c)**(2)*cos(B)*cos(C))', ID="X_2969", classes=["center"])
            X_2973 = cevapoint(model, A, B, C, X_1986, X_2969, ID="X_2973", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_150 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(4) + c**(4) - a**(4) + a*(b*c**(2) +c*b**(2) - b**(3) - c**(3)) - b*c*(a**(2) + b**(2) + c**(2)) + (b + c)*a**(3)))', ID="X_150", classes=["center", "incident"])
            central_line(model, X_4, X_150, 4, 150, incident=True)
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_675 = eval_trilinear_point(model, A, B, C, '(b*c/(b**(3) + c**(3) - a*(b**(2) + c**(2))))', ID="X_675", classes=["center", "incident"])
            central_line(model, X_25, X_675, 25, 675, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_917 = eval_trilinear_point(model, A, B, C, '(sec(A))/((a - b)*sin(2*B) + (a - c)*sin(2*C))', ID="X_917", classes=["center", "incident"])
            central_line(model, X_3, X_917, 3, 917, incident=True)
            return promote_point_to_top(model, X_2973)


        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_2973 on the given reference triangle."""
            model = create_model('X_2973 = 7th MACBEATH POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02973(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-02973.json"))
            write_center_svg(
                model_acute,
                here / "x-02973.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2973¶

X₂₉₇₃¶