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X₃₈₀₅¶

X₂₇₈₆com[INVERSE(nT(bc,c²))]

X₃₈₀₅ = crossdifference of every pair of points on line X₆ X₂₅₆

X₃₈₀₅ (X₂₇₈₆com[INVERSE(nT(bc,c²))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3805 = X_2786com[INVERSE(nT(bc,c²))]."""

        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,
            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_03805(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3805 = X_2786com[INVERSE(nT(bc,c²))] on reference triangle ABC."""
            X_3805 = eval_barycentric_point(model, A, B, C, 'a*(b - c)*(a**(2) + b*c)*(b**(2) + c**(2) + b*c)', ID="X_3805", classes=["selected", "target"])
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            central_line(model, X_30, X_511, 30, 511, incident=True)
            X_38 = eval_trilinear_point(model, A, B, C, 'b**(2) + c**(2)', ID="X_38", classes=["center", "incident"])
            X_661 = eval_trilinear_point(model, A, B, C, 'cot(B) - cot(C)', ID="X_661", classes=["center", "incident"])
            central_line(model, X_38, X_661, 38, 661, incident=True)
            return promote_point_to_top(model, X_3805)


        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_3805 on the given reference triangle."""
            model = create_model('X_3805 = X_2786com[INVERSE(nT(bc,c²))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03805(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-03805.json"))
            write_center_svg(
                model_acute,
                here / "x-03805.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3805¶

X₃₈₀₅¶