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X₆₈₂¶

POINT ARNEB

X₆₈₂ (POINT ARNEB) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_682 = POINT ARNEB."""

        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,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00682(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_682 = POINT ARNEB on reference triangle ABC."""
            X_682 = eval_trilinear_point(model, A, B, C, '(sec(B)*(csc(C))**(3) + sec(C)*(csc(B))**(3))', ID="X_682", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            central_line(model, X_3, X_69, 3, 69, incident=True)
            X_154 = eval_trilinear_point(model, A, B, C, '(cos(A) - cos(B)*cos(C))*a**(2)', ID="X_154", classes=["center", "incident"])
            X_237 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A +  omega  )', ID="X_237", classes=["center", "incident"])
            central_line(model, X_154, X_237, 154, 237, incident=True)
            X_248 = eval_trilinear_point(model, A, B, C, 'sin(2*A)*sec(A +  omega  )', ID="X_248", classes=["center", "incident"])
            X_695 = eval_trilinear_point(model, A, B, C, 'a/(a**(4) + b**(2)*c**(2))', ID="X_695", classes=["center", "incident"])
            central_line(model, X_248, X_695, 248, 695, incident=True)
            return promote_point_to_top(model, X_682)


        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_682 on the given reference triangle."""
            model = create_model('X_682 = POINT ARNEB')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00682(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-00682.json"))
            write_center_svg(
                model_acute,
                here / "x-00682.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X682¶

X₆₈₂¶