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X₂₁₆₇¶

X₂-ISOCONJUGATE OF X₅₁

X₂₁₆₇ (X₂-ISOCONJUGATE OF X₅₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2167 = X_2-ISOCONJUGATE OF X_51."""

        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_02167(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2167 = X_2-ISOCONJUGATE OF X_51 on reference triangle ABC."""
            X_1953 = eval_trilinear_point(model, A, B, C, 'sin(2*B) + sin(2*C)', ID="X_1953", classes=["center"])
            X_2167 = isogonal_conjugate(model, A, B, C, X_1953, ID="X_2167", classes=["selected", "target"])
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center", "incident"])
            X_72 = eval_trilinear_point(model, A, B, C, '(b + c)*cot(A)', ID="X_72", classes=["center", "incident"])
            central_line(model, X_54, X_72, 54, 72, incident=True)
            X_48 = eval_trilinear_point(model, A, B, C, 'tan(B) + tan(C)', ID="X_48", classes=["center", "incident"])
            X_92 = eval_trilinear_point(model, A, B, C, 'csc(2*A)', ID="X_92", classes=["center", "incident"])
            central_line(model, X_48, X_92, 48, 92, incident=True)
            X_38 = eval_trilinear_point(model, A, B, C, 'b**(2) + c**(2)', ID="X_38", classes=["center", "incident"])
            X_293 = eval_trilinear_point(model, A, B, C, 'cos(A)*sec(A +  omega  )', ID="X_293", classes=["center", "incident"])
            central_line(model, X_38, X_293, 38, 293, incident=True)
            return promote_point_to_top(model, X_2167)


        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_2167 on the given reference triangle."""
            model = create_model('X_2167 = X_2-ISOCONJUGATE OF X_51')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02167(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-02167.json"))
            write_center_svg(
                model_acute,
                here / "x-02167.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2167¶

X₂₁₆₇¶