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X₁₄₀₉¶

X₇₁-BETH CONJUGATE OF X₇₁

X₁₄₀₉ (X₇₁-BETH CONJUGATE OF X₇₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1409 = X_71-BETH CONJUGATE OF X_71."""

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


        def construct_x_01409(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1409 = X_71-BETH CONJUGATE OF X_71 on reference triangle ABC."""
            X_1409 = eval_trilinear_point(model, A, B, C, 'a*(sec(B) + sec(C))', ID="X_1409", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            central_line(model, X_6, X_19, 6, 19, incident=True)
            X_63 = eval_trilinear_point(model, A, B, C, 'cot(A)', ID="X_63", classes=["center", "incident"])
            X_77 = eval_trilinear_point(model, A, B, C, '1/(1 + sec(A))', ID="X_77", classes=["center", "incident"])
            central_line(model, X_63, X_77, 63, 77, incident=True)
            X_71 = eval_trilinear_point(model, A, B, C, '(b + c)*cos(A)', ID="X_71", classes=["center", "incident"])
            X_73 = eval_trilinear_point(model, A, B, C, 'sec(B) + sec(C)', ID="X_73", classes=["center", "incident"])
            central_line(model, X_71, X_73, 71, 73, incident=True)
            return promote_point_to_top(model, X_1409)


        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_1409 on the given reference triangle."""
            model = create_model('X_1409 = X_71-BETH CONJUGATE OF X_71')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01409(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-01409.json"))
            write_center_svg(
                model_acute,
                here / "x-01409.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1409¶

X₁₄₀₉¶