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X₃₁₁₄¶

TgX(32)

X₃₁₁₄ = trilinear pole of line X₆₆₉ X₈₀₄

X₃₁₁₄ (TgX(32)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3114 = TgX(32)."""

        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_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03114(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3114 = TgX(32) on reference triangle ABC."""
            X_3114 = eval_trilinear_point(model, A, B, C, '1/(a**(3)*(b**(4) + c**(4) + b**(2)*c**(2)))', ID="X_3114", classes=["selected", "target"])
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", classes=["center", "incident"])
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            central_line(model, X_32, X_76, 32, 76, incident=True)
            X_183 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)*cos(A-  omega  )', ID="X_183", classes=["center", "incident"])
            X_327 = eval_trilinear_point(model, A, B, C, '(csc(A))**(2)*sec(A -  omega  )', ID="X_327", classes=["center", "incident"])
            central_line(model, X_183, X_327, 183, 327, incident=True)
            X_264 = eval_trilinear_point(model, A, B, C, 'csc(A)*csc(2*A)', ID="X_264", classes=["center", "incident"])
            X_419 = eval_barycentric_point(model, A, B, C, '(a**(2) - b*c) * (a**(2) + b*c) * (a**(2) + b**(2) - c**(2)) * (a**(2) - b**(2) + c**(2))', ID="X_419", classes=["center", "incident"])
            central_line(model, X_264, X_419, 264, 419, incident=True)
            return promote_point_to_top(model, X_3114)


        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_3114 on the given reference triangle."""
            model = create_model('X_3114 = TgX(32)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03114(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-03114.json"))
            write_center_svg(
                model_acute,
                here / "x-03114.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3114¶

X₃₁₁₄¶