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X₂₁₆₆¶

X₂-ISOCONJUGATE OF X₅₀

X₂₁₆₆ = trilinear pole of line X₆₆₁ X₁₉₅₃

X₂₁₆₆ (X₂-ISOCONJUGATE OF X₅₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2166 = X_2-ISOCONJUGATE OF X_50."""

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


        def construct_x_02166(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2166 = X_2-ISOCONJUGATE OF X_50 on reference triangle ABC."""
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_1749 = eval_trilinear_point(model, A, B, C, 'a**(6) - 3*a**(4)*(b**(2) + c**(2)) + a**(2)*(3*b**(4) - b**(2)*c**(2) + 3*c**(4)) - (b**(2) - c**(2))**(2)*(b**(2) + c**(2))', ID="X_1749", classes=["center"])
            X_2166 = cevapoint(model, A, B, C, X_1, X_1749, ID="X_2166", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_94 = eval_trilinear_point(model, A, B, C, 'csc(3*A)', ID="X_94", classes=["center", "incident"])
            central_line(model, X_10, X_94, 10, 94, incident=True)
            X_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
            X_79 = eval_trilinear_point(model, A, B, C, '1/(1 + 2*cos(A))', ID="X_79", classes=["center", "incident"])
            central_line(model, X_65, X_79, 65, 79, incident=True)
            X_564 = eval_trilinear_point(model, A, B, C, 'cos(2*B - 2*C)', ID="X_564", classes=["center", "incident"])
            central_line(model, X_1, X_564, 1, 564, incident=True)
            return promote_point_to_top(model, X_2166)


        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_2166 on the given reference triangle."""
            model = create_model('X_2166 = X_2-ISOCONJUGATE OF X_50')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02166(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-02166.json"))
            write_center_svg(
                model_acute,
                here / "x-02166.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2166¶

X₂₁₆₆¶