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X₃₄₀₆¶

SEC(A + 2ω) POINT

X₃₄₀₆ and related points occupy Bernard Gibert’s Table 38. See the note at X₃₃₆₄.

X₃₄₀₆ (SEC(A + 2ω) POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3406 = SEC(A + 2ω) 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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            isogonal_conjugate,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03406(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3406 = SEC(A + 2ω) POINT on reference triangle ABC."""
            X_3095 = eval_trilinear_point(model, A, B, C, 'cos(A + 2*omega  )', ID="X_3095", classes=["center"])
            X_3406 = isogonal_conjugate(model, A, B, C, X_3095, ID="X_3406", classes=["selected", "target"])
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            X_182 = eval_trilinear_point(model, A, B, C, 'cos(A-  omega  )', ID="X_182", classes=["center", "incident"])
            central_line(model, X_76, X_182, 76, 182, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_1691 = eval_trilinear_point(model, A, B, C, 'sin(A - 2*omega  )', ID="X_1691", classes=["center", "incident"])
            central_line(model, X_4, X_1691, 4, 1691, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_1916 = eval_trilinear_point(model, A, B, C, 'b*c/(a**(4) - b**(2)*c**(2))', ID="X_1916", classes=["center", "incident"])
            central_line(model, X_3, X_1916, 3, 1916, incident=True)
            return promote_point_to_top(model, X_3406)


        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_3406 on the given reference triangle."""
            model = create_model('X_3406 = SEC(A + 2ω) POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03406(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-03406.json"))
            write_center_svg(
                model_acute,
                here / "x-03406.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3406¶

X₃₄₀₆¶