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X₂₆₀₈¶

TRILINEAR POLE OF PU(70)

X₂₆₀₈ = point of intersection, other than A, B, C, of 1st and 2nd bicentrics of the Kiepert hyperbola

X₂₆₀₈ (TRILINEAR POLE OF PU(70)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2608 = TRILINEAR POLE OF PU(70)."""

        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_trilinear_point,
            incenter_of,
            isogonal_conjugate,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02608(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2608 = TRILINEAR POLE OF PU(70) on reference triangle ABC."""
            X_2607 = eval_trilinear_point(model, A, B, C, 'sin(A - B)*sin(A - C) + (sin(B - C))**(2)', ID="X_2607", classes=["center"])
            X_2608 = isogonal_conjugate(model, A, B, C, X_2607, ID="X_2608", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_2614 = eval_trilinear_point(model, A, B, C, '(1/(csc(A - B)*csc(A - C) + (csc(B - C))**(2)))', ID="X_2614", classes=["center", "incident"])
            central_line(model, X_1, X_2614, 1, 2614, incident=True)
            X_2606 = eval_trilinear_point(model, A, B, C, 'sin(A - B)*sin(A - C) - (sin(B - C))**(2)', ID="X_2606", classes=["center", "incident"])
            X_2611 = point_from_barycentrics(model, A, B, C, 0.21464646, 0.68065268, 0.10470085, ID="X_2611", classes=["center", "incident"])
            central_line(model, X_2606, X_2611, 2606, 2611, incident=True)
            return promote_point_to_top(model, X_2608)


        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_2608 on the given reference triangle."""
            model = create_model('X_2608 = TRILINEAR POLE OF PU(70)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02608(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-02608.json"))
            write_center_svg(
                model_acute,
                here / "x-02608.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2608¶

X₂₆₀₈¶