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X₂₉₈₁¶

DC(X₁₃)

X₂₉₈₁ = perspector of ABC and unary cofactor triangle of outer Napoleon triangle

X₂₉₈₁ (DC(X₁₃)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2981 = DC(X_13)."""

        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,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02981(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2981 = DC(X_13) on reference triangle ABC."""
            X_396 = eval_trilinear_point(model, A, B, C, 'cos(B - C) + 2*cos(A -  pi  /3)', ID="X_396", classes=["center"])
            X_2981 = isogonal_conjugate(model, A, B, C, X_396, ID="X_2981", classes=["selected", "target"])
            X_61 = eval_trilinear_point(model, A, B, C, 'sin(A +  pi  /6)', ID="X_61", classes=["center", "incident"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_61, X_110, 61, 110, incident=True)
            X_15 = eval_trilinear_point(model, A, B, C, 'sin(A +  pi  /3)', ID="X_15", classes=["center", "incident"])
            X_1337 = eval_barycentric_point(model, A, B, C, '(a**(2)*(2*D*U - 3**(1/2)*V*W)/(4*D + 3**(1/2)*a**(2)))', ID="X_1337", classes=["center", "incident"])
            central_line(model, X_15, X_1337, 15, 1337, incident=True)
            X_1989 = eval_trilinear_point(model, A, B, C, '(sin(A))**(2)*csc(3*A)', ID="X_1989", classes=["center", "incident"])
            central_line(model, X_396, X_1989, 396, 1989, incident=True)
            return promote_point_to_top(model, X_2981)


        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_2981 on the given reference triangle."""
            model = create_model('X_2981 = DC(X_13)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02981(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-02981.json"))
            write_center_svg(
                model_acute,
                here / "x-02981.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2981¶

X₂₉₈₁¶