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X₂₉₇₂¶

6th MACBEATH POINT

X₂₉₇₂ = crossdifference of every pair of points on line X₁₀₇ X₁₁₂

X₂₉₇₂ (6th MACBEATH POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2972 = 6th 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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02972(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2972 = 6th MACBEATH POINT on reference triangle ABC."""
            X_2972 = eval_trilinear_point(model, A, B, C, '((b*c*(b**(2) - c**(2)))**(2)*(cos(A))**(3))', ID="X_2972", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", 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_3, X_74, 3, 74, incident=True)
            X_122 = eval_trilinear_point(model, A, B, C, '(b**(2) - c**(2))**(2)*(cos(A) - cos(B)*cos(C))*(cot(A))**(2)', ID="X_122", classes=["center", "incident"])
            X_125 = eval_trilinear_point(model, A, B, C, 'cos(A)*(sin(B - C))**(2)', ID="X_125", classes=["center", "incident"])
            central_line(model, X_122, X_125, 122, 125, incident=True)
            X_127 = eval_trilinear_point(model, A, B, C, 'b*c*(sin(2*B) - sin(2*C))*((b**(2) - c**(2))*sin(2*A) - b**(2)*sin(2*B) + c**(2)*sin(2*C))', ID="X_127", classes=["center", "incident"])
            X_136 = eval_barycentric_point(model, A, B, C, '(b**(2) - c**(2))**(2)*(a**(4) + b**(4) + c**(4) - 2*a**(2)*b**(2) - 2*a**(2)*c**(2))/(a**(2) - b**(2) - c**(2))', ID="X_136", classes=["center", "incident"])
            central_line(model, X_127, X_136, 127, 136, incident=True)
            return promote_point_to_top(model, X_2972)


        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_2972 on the given reference triangle."""
            model = create_model('X_2972 = 6th MACBEATH POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02972(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-02972.json"))
            write_center_svg(
                model_acute,
                here / "x-02972.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2972¶

X₂₉₇₂¶