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X₆₇₀¶

TRILINEAR POLE OF LINE X₂X_39

X₆₇₀ (TRILINEAR POLE OF LINE X₂X_39) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_670 = TRILINEAR POLE OF LINE X_2X_39."""

        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_00670(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_670 = TRILINEAR POLE OF LINE X_2X_39 on reference triangle ABC."""
            X_669 = eval_trilinear_point(model, A, B, C, 'a**(3)*(b**(2) - c**(2))', ID="X_669", classes=["center"])
            X_670 = isogonal_conjugate(model, A, B, C, X_669, ID="X_670", classes=["selected", "target"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            X_290 = eval_trilinear_point(model, A, B, C, '(csc(A))**(2)*sec(A +  omega  )', ID="X_290", classes=["center", "incident"])
            central_line(model, X_69, X_290, 69, 290, incident=True)
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            X_338 = eval_trilinear_point(model, A, B, C, '(b**(2) - c**(2))**(2)/a**(3)', ID="X_338", classes=["center", "incident"])
            central_line(model, X_76, X_338, 76, 338, incident=True)
            X_141 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) + c**(2))', ID="X_141", 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_141, X_308, 141, 308, incident=True)
            return promote_point_to_top(model, X_670)


        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_670 on the given reference triangle."""
            model = create_model('X_670 = TRILINEAR POLE OF LINE X_2X_39')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00670(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-00670.json"))
            write_center_svg(
                model_acute,
                here / "x-00670.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X670¶

X₆₇₀¶