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X₆₆₆¶

TRILINEAR POLE OF LINE X₂X_11

X₆₆₆ (TRILINEAR POLE OF LINE X₂X_11) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_666 = TRILINEAR POLE OF LINE X_2X_11."""

        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_00666(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_666 = TRILINEAR POLE OF LINE X_2X_11 on reference triangle ABC."""
            X_665 = eval_trilinear_point(model, A, B, C, 'a*((a - b)**(2)*(a + b - c) - (c - a)**(2)*(c + a - b))', ID="X_665", classes=["center"])
            X_666 = isogonal_conjugate(model, A, B, C, X_665, ID="X_666", classes=["selected", "target"])
            X_239 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2) - b*c)', ID="X_239", classes=["center", "incident"])
            X_294 = eval_trilinear_point(model, A, B, C, '((b + c - a)/(b**(2) + c**(2) - a*b - a*c))', ID="X_294", classes=["center", "incident"])
            central_line(model, X_239, X_294, 239, 294, incident=True)
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            X_514 = eval_trilinear_point(model, A, B, C, '(b - c)/a', ID="X_514", classes=["center", "incident"])
            central_line(model, X_101, X_514, 101, 514, incident=True)
            X_190 = eval_trilinear_point(model, A, B, C, 'b*c/(b - c)', ID="X_190", classes=["center", "incident"])
            X_522 = eval_trilinear_point(model, A, B, C, '(cos(B) - cos(C))*(csc(A))', ID="X_522", classes=["center", "incident"])
            central_line(model, X_190, X_522, 190, 522, incident=True)
            return promote_point_to_top(model, X_666)


        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_666 on the given reference triangle."""
            model = create_model('X_666 = TRILINEAR POLE OF LINE X_2X_11')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00666(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-00666.json"))
            write_center_svg(
                model_acute,
                here / "x-00666.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X666¶

X₆₆₆¶