← etc / Encyclopedia of Triangle Centers

X₂₆₅₈¶

SUM OF PU(83)

X₂₆₅₈ (SUM OF PU(83)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2658 = SUM OF PU(83)."""

        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,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02658(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2658 = SUM OF PU(83) on reference triangle ABC."""
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_2654 = eval_trilinear_point(model, A, B, C, '2*sec(A) + sec(B) + sec(C)', ID="X_2654", classes=["center"])
            X_2658 = ceva_conjugate(model, A, B, C, X_1, X_2654, ID="X_2658", classes=["selected", "target"])
            X_29 = eval_trilinear_point(model, A, B, C, '(sec(A))/(cos(B) + cos(C))', ID="X_29", classes=["center", "incident"])
            central_line(model, X_1, X_29, 1, 29, incident=True)
            X_42 = eval_trilinear_point(model, A, B, C, 'a*(b + c)', ID="X_42", classes=["center", "incident"])
            X_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
            central_line(model, X_42, X_65, 42, 65, incident=True)
            X_1108 = point_from_barycentrics(model, A, B, C, 0.16604303, 0.31992516, 0.51403181, ID="X_1108", classes=["center", "incident"])
            X_1201 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) + c**(2) - 2*b*c + a*b + a*c))', ID="X_1201", classes=["center", "incident"])
            central_line(model, X_1108, X_1201, 1108, 1201, incident=True)
            return promote_point_to_top(model, X_2658)


        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_2658 on the given reference triangle."""
            model = create_model('X_2658 = SUM OF PU(83)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02658(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-02658.json"))
            write_center_svg(
                model_acute,
                here / "x-02658.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2658¶

X₂₆₅₈¶