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X₃₃₉₉¶

SEC(A - 2ω) POINT

X₃₃₉₉ and related points occupy Bernard Gibert’s Table 38. See the note at X₃₃₆₄.

X₃₃₉₉ (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_3399 = 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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            isogonal_conjugate,
            nine_point_center_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03399(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3399 = SEC(A - 2ω) POINT on reference triangle ABC."""
            X_3398 = eval_trilinear_point(model, A, B, C, 'cos(A - 2*omega  )', ID="X_3398", classes=["center"])
            X_3399 = isogonal_conjugate(model, A, B, C, X_3398, ID="X_3399", classes=["selected", "target"])
            X_262 = eval_trilinear_point(model, A, B, C, 'sec(A -  omega  )', ID="X_262", classes=["center", "incident"])
            X_1506 = eval_trilinear_point(model, A, B, C, 'b*c*((b**(2) - c**(2))**(2) - 2*a**(2)*(b**(2) + c**(2)))', ID="X_1506", classes=["center", "incident"])
            central_line(model, X_262, X_1506, 262, 1506, incident=True)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", 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_5, X_1916, 5, 1916, incident=True)
            X_597 = eval_trilinear_point(model, A, B, C, '(4*a**(2) + b**(2) + c**(2))/a', ID="X_597", classes=["center", "incident"])
            X_1576 = eval_trilinear_point(model, A, B, C, 'a**(3)/(b**(2) - c**(2))', ID="X_1576", classes=["center", "incident"])
            central_line(model, X_597, X_1576, 597, 1576, incident=True)
            return promote_point_to_top(model, X_3399)


        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_3399 on the given reference triangle."""
            model = create_model('X_3399 = SEC(A - 2ω) POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03399(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-03399.json"))
            write_center_svg(
                model_acute,
                here / "x-03399.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3399¶

X₃₃₉₉¶