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X₁₉₂₇¶

TRILINEAR POLE OF PU(13)

X₁₉₂₇ = cevapoint of X₁₉₃₂ and X₁₉₃₃

X₁₉₂₇ (TRILINEAR POLE OF PU(13)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1927 = TRILINEAR POLE OF PU(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_trilinear_point,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01927(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1927 = TRILINEAR POLE OF PU(13) on reference triangle ABC."""
            X_1926 = eval_trilinear_point(model, A, B, C, '(1 - b**(2)*c**(2)/a**(4))', ID="X_1926", classes=["center"])
            X_1927 = isogonal_conjugate(model, A, B, C, X_1926, ID="X_1927", classes=["selected", "target"])
            X_82 = eval_trilinear_point(model, A, B, C, '1/(b**(2) + c**(2))', ID="X_82", classes=["center", "incident"])
            X_662 = eval_trilinear_point(model, A, B, C, '1/(cot(B) - cot(C))', ID="X_662", classes=["center", "incident"])
            central_line(model, X_82, X_662, 82, 662, incident=True)
            X_172 = eval_trilinear_point(model, A, B, C, 'a**(3) + a*b*c', ID="X_172", classes=["center", "incident"])
            X_694 = eval_trilinear_point(model, A, B, C, 'a/(a**(4) - b**(2)*c**(2))', ID="X_694", classes=["center", "incident"])
            central_line(model, X_172, X_694, 172, 694, incident=True)
            X_715 = eval_trilinear_point(model, A, B, C, '(1/(a **(-4)*(b **(-1) + c **(-1)) - a **(-2)*(b **(-3) + c **(-3))))', ID="X_715", classes=["center", "incident"])
            X_805 = eval_trilinear_point(model, A, B, C, '(1/(a **(-3)*(b**(2) - c**(2)) + a**(1)*(b **(-2) - c **(-2))))', ID="X_805", classes=["center", "incident"])
            central_line(model, X_715, X_805, 715, 805, incident=True)
            return promote_point_to_top(model, X_1927)


        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_1927 on the given reference triangle."""
            model = create_model('X_1927 = TRILINEAR POLE OF PU(13)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01927(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-01927.json"))
            write_center_svg(
                model_acute,
                here / "x-01927.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1927¶

X₁₉₂₇¶