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X₂₁₆₉¶

X₂-ISOCONJUGATE OF X₅₃

X₂₁₆₉ (X₂-ISOCONJUGATE OF X₅₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2169 = X_2-ISOCONJUGATE OF X_53."""

        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,
            ceva_conjugate,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02169(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2169 = X_2-ISOCONJUGATE OF X_53 on reference triangle ABC."""
            X_2167 = eval_trilinear_point(model, A, B, C, '(1/(sin(2*B) + sin(2*C)))', ID="X_2167", classes=["center"])
            X_2148 = eval_trilinear_point(model, A, B, C, 'a*sec(B - C)', ID="X_2148", classes=["center"])
            X_2169 = ceva_conjugate(model, A, B, C, X_2167, X_2148, ID="X_2169", classes=["selected", "target"])
            X_36 = eval_trilinear_point(model, A, B, C, '1 - 2*cos(A)', ID="X_36", classes=["center", "incident"])
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center", "incident"])
            central_line(model, X_36, X_54, 36, 54, incident=True)
            X_47 = eval_trilinear_point(model, A, B, C, 'cos(2*A)', ID="X_47", classes=["center", "incident"])
            X_48 = eval_trilinear_point(model, A, B, C, 'tan(B) + tan(C)', ID="X_48", classes=["center", "incident"])
            central_line(model, X_47, X_48, 47, 48, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_1748 = eval_trilinear_point(model, A, B, C, 'cot(A) - tan(A)', ID="X_1748", classes=["center", "incident"])
            central_line(model, X_1, X_1748, 1, 1748, incident=True)
            return promote_point_to_top(model, X_2169)


        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_2169 on the given reference triangle."""
            model = create_model('X_2169 = X_2-ISOCONJUGATE OF X_53')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02169(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-02169.json"))
            write_center_svg(
                model_acute,
                here / "x-02169.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2169¶

X₂₁₆₉¶