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X₃₅₉₀¶

1st DIXIT POINT

The radius of circle T_A is |BC|/6, and the Kiepert angle (e.g., B-to-C-to-X₃₈₉₀) is arctan(2/3).

X₃₅₉₀ (1st DIXIT POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3590 = 1st DIXIT 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,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03590(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3590 = 1st DIXIT POINT on reference triangle ABC."""
            X_3590 = eval_trilinear_point(model, A, B, C, '(b*c/(b**(2) + c**(2) - a**(2) + 6*area ))', ID="X_3590", classes=["selected", "target"])
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center", "incident"])
            X_1327 = eval_trilinear_point(model, A, B, C, '(1/(sin(A) + 3*cos(A)))', ID="X_1327", classes=["center", "incident"])
            central_line(model, X_20, X_1327, 20, 1327, incident=True)
            X_590 = eval_trilinear_point(model, A, B, C, '(a**(2) + 4*area )/a', ID="X_590", classes=["center", "incident"])
            X_1131 = eval_trilinear_point(model, A, B, C, '1/(sin(A) + 2*cos(A))', ID="X_1131", classes=["center", "incident"])
            central_line(model, X_590, X_1131, 590, 1131, incident=True)
            X_140 = eval_trilinear_point(model, A, B, C, '2*cos(A) + cos(B - C)', ID="X_140", classes=["center", "incident"])
            X_3316 = eval_trilinear_point(model, A, B, C, '1/(cos(A) + 2*sin(A))', ID="X_3316", classes=["center", "incident"])
            central_line(model, X_140, X_3316, 140, 3316, incident=True)
            return promote_point_to_top(model, X_3590)


        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_3590 on the given reference triangle."""
            model = create_model('X_3590 = 1st DIXIT POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03590(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-03590.json"))
            write_center_svg(
                model_acute,
                here / "x-03590.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3590¶

X₃₅₉₀¶