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X₂₅₉₉¶

SUM OF PU(69)

X₂₅₉₉ (SUM OF PU(69)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2599 = SUM OF PU(69)."""

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


        def construct_x_02599(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2599 = SUM OF PU(69) on reference triangle ABC."""
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_2594 = eval_trilinear_point(model, A, B, C, '(cos(C- A) + cos(B - A))', ID="X_2594", classes=["center"])
            X_2599 = ceva_conjugate(model, A, B, C, X_1, X_2594, ID="X_2599", classes=["selected", "target"])
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center", "incident"])
            central_line(model, X_1, X_54, 1, 54, incident=True)
            X_35 = eval_trilinear_point(model, A, B, C, '1 + 2*cos(A)', ID="X_35", classes=["center", "incident"])
            X_186 = eval_trilinear_point(model, A, B, C, '4*cos(A) - sec(A)', ID="X_186", classes=["center", "incident"])
            central_line(model, X_35, X_186, 35, 186, incident=True)
            X_12 = eval_trilinear_point(model, A, B, C, '1 + cos(B - C)', ID="X_12", classes=["center", "incident"])
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center", "incident"])
            central_line(model, X_12, X_523, 12, 523, incident=True)
            return promote_point_to_top(model, X_2599)


        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_2599 on the given reference triangle."""
            model = create_model('X_2599 = SUM OF PU(69)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02599(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-02599.json"))
            write_center_svg(
                model_acute,
                here / "x-02599.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2599¶

X₂₅₉₉¶