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X₂₉₈₆¶

DC(X₇₄)

X₂₉₈₆ = trilinear pole of line X₃ X₅₂₃ (the line of the Ehrmann cross-triangle)

X₂₉₈₆ (DC(X₇₄)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2986 = DC(X_74)."""

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


        def construct_x_02986(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2986 = DC(X_74) on reference triangle ABC."""
            X_2986 = eval_barycentric_point(model, A, B, C, '1/(1 + cos(2*B) + cos(2*C))', ID="X_2986", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", 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_4, X_110, 4, 110, incident=True)
            X_94 = eval_trilinear_point(model, A, B, C, 'csc(3*A)', ID="X_94", classes=["center", "incident"])
            X_323 = eval_trilinear_point(model, A, B, C, 'sin(3*A)*(csc(A))**(2)', ID="X_323", classes=["center", "incident"])
            central_line(model, X_94, X_323, 94, 323, incident=True)
            X_338 = eval_trilinear_point(model, A, B, C, '(b**(2) - c**(2))**(2)/a**(3)', ID="X_338", classes=["center", "incident"])
            X_394 = eval_trilinear_point(model, A, B, C, 'cos(A)*cot(A)', ID="X_394", classes=["center", "incident"])
            central_line(model, X_338, X_394, 338, 394, incident=True)
            return promote_point_to_top(model, X_2986)


        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_2986 on the given reference triangle."""
            model = create_model('X_2986 = DC(X_74)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02986(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-02986.json"))
            write_center_svg(
                model_acute,
                here / "x-02986.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2986¶

X₂₉₈₆¶