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X₂₉₆₈¶

2nd MACBEATH POINT

X₂₉₆₈ (2nd MACBEATH POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2968 = 2nd 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,
            complement,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            feuerbach_point_of,
            nagel_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02968(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2968 = 2nd MACBEATH POINT on reference triangle ABC."""
            X_1897 = eval_trilinear_point(model, A, B, C, '(sec(A))/(b - c)', ID="X_1897", classes=["center"])
            X_2968 = complement(model, A, B, C, X_1897, ID="X_2968", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            central_line(model, X_3, X_8, 3, 8, incident=True)
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_123 = eval_trilinear_point(model, A, B, C, '(csc(A))*(sec(B) - sec(C))*((sec(A))*((sin(B))**(2) - (sin(C))**(2)) + sin(C)*tan(C) - sin(B)*tan(B))', ID="X_123", classes=["center", "incident"])
            central_line(model, X_11, X_123, 11, 123, incident=True)
            X_116 = eval_trilinear_point(model, A, B, C, 'b*c*((b - c)**(2)*(b**(2) + b*c + c**(2) - a*b - a*c))', ID="X_116", classes=["center", "incident"])
            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"])
            central_line(model, X_116, X_122, 116, 122, incident=True)
            return promote_point_to_top(model, X_2968)


        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_2968 on the given reference triangle."""
            model = create_model('X_2968 = 2nd MACBEATH POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02968(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-02968.json"))
            write_center_svg(
                model_acute,
                here / "x-02968.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2968¶

X₂₉₆₈¶