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X₁₉₆₇¶

TRILINEAR POLE OF PU(36)

X₁₉₆₇ = cevapoint of X₁₅₈₀ and X₁₅₈₂

X₁₉₆₇ (TRILINEAR POLE OF PU(36)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1967 = TRILINEAR POLE OF PU(36)."""

        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_01967(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1967 = TRILINEAR POLE OF PU(36) on reference triangle ABC."""
            X_1966 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)*(a**(4) - b**(2)*c**(2))', ID="X_1966", classes=["center"])
            X_1967 = isogonal_conjugate(model, A, B, C, X_1966, ID="X_1967", classes=["selected", "target"])
            X_256 = eval_trilinear_point(model, A, B, C, '1/(a**(2) + b*c)', ID="X_256", classes=["center", "incident"])
            X_291 = eval_trilinear_point(model, A, B, C, '1/(a**(2) - b*c)', ID="X_291", classes=["center", "incident"])
            central_line(model, X_256, X_291, 256, 291, incident=True)
            X_42 = eval_trilinear_point(model, A, B, C, 'a*(b + c)', ID="X_42", 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_42, X_694, 42, 694, incident=True)
            X_38 = eval_trilinear_point(model, A, B, C, 'b**(2) + c**(2)', ID="X_38", classes=["center", "incident"])
            X_799 = eval_trilinear_point(model, A, B, C, '(csc(A))**(2)/((cos(B))**(2) - (cos(C))**(2))', ID="X_799", classes=["center", "incident"])
            central_line(model, X_38, X_799, 38, 799, incident=True)
            return promote_point_to_top(model, X_1967)


        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_1967 on the given reference triangle."""
            model = create_model('X_1967 = TRILINEAR POLE OF PU(36)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01967(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-01967.json"))
            write_center_svg(
                model_acute,
                here / "x-01967.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1967¶

X₁₉₆₇¶