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X₆₈₉¶

TRILINEAR POLE OF LINE X₆X_76

X₆₈₉ = Ψ(X₃₂, X₂)

X₆₈₉ (TRILINEAR POLE OF LINE X₆X_76) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_689 = TRILINEAR POLE OF LINE X_6X_76."""

        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,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00689(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_689 = TRILINEAR POLE OF LINE X_6X_76 on reference triangle ABC."""
            X_688 = eval_trilinear_point(model, A, B, C, '(a**(3)*(b**(4) - c**(4)))', ID="X_688", classes=["center"])
            X_689 = isogonal_conjugate(model, A, B, C, X_688, ID="X_689", classes=["selected", "target"])
            X_111 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(2) - b**(2) - c**(2))', ID="X_111", classes=["center", "incident"])
            X_308 = eval_trilinear_point(model, A, B, C, 'b**(3)*c**(3)/(b**(2) + c**(2))', ID="X_308", classes=["center", "incident"])
            central_line(model, X_111, X_308, 111, 308, incident=True)
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            X_670 = eval_trilinear_point(model, A, B, C, '1/(a**(3)*(b**(2) - c**(2)))', ID="X_670", classes=["center", "incident"])
            central_line(model, X_110, X_670, 110, 670, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_703 = eval_trilinear_point(model, A, B, C, '(1/(a **(-5)*(b**(0) + c**(0)) - a **(-1)*(b **(-4) + c **(-4))))', ID="X_703", classes=["center", "incident"])
            central_line(model, X_6, X_703, 6, 703, incident=True)
            return promote_point_to_top(model, X_689)


        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_689 on the given reference triangle."""
            model = create_model('X_689 = TRILINEAR POLE OF LINE X_6X_76')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00689(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-00689.json"))
            write_center_svg(
                model_acute,
                here / "x-00689.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X689¶

X₆₈₉¶