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X₃₄₀₅¶

COT(A + ω) POINT

X₃₄₀₅ and related points occupy Bernard Gibert’s Table 38. See the note at X₃₃₆₄.

X₃₄₀₅ (COT(A + ω) POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3405 = COT(A + ω) POINT."""

        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,
            incenter_of,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03405(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3405 = COT(A + ω) POINT on reference triangle ABC."""
            X_3404 = eval_trilinear_point(model, A, B, C, '(tan(A +  omega  ))', ID="X_3404", classes=["center"])
            X_3405 = isogonal_conjugate(model, A, B, C, X_3404, ID="X_3405", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_82 = eval_trilinear_point(model, A, B, C, '1/(b**(2) + c**(2))', ID="X_82", classes=["center", "incident"])
            central_line(model, X_1, X_82, 1, 82, incident=True)
            X_798 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b**(2) - c**(2))', ID="X_798", classes=["center", "incident"])
            X_812 = eval_trilinear_point(model, A, B, C, 'a **(-2)*(b**(1) - c**(1)) + a**(0)*(b **(-1) - c **(-1))', ID="X_812", classes=["center", "incident"])
            central_line(model, X_798, X_812, 798, 812, incident=True)
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            X_1969 = eval_trilinear_point(model, A, B, C, '(b**(2)*c**(2)*sin(2*B)*sin(2*C))', ID="X_1969", classes=["center", "incident"])
            central_line(model, X_19, X_1969, 19, 1969, incident=True)
            return promote_point_to_top(model, X_3405)


        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_3405 on the given reference triangle."""
            model = create_model('X_3405 = COT(A + ω) POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03405(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-03405.json"))
            write_center_svg(
                model_acute,
                here / "x-03405.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3405¶

X₃₄₀₅¶