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X₂₅₉₄¶

SUM OF PU(68)

The notation “PU(68)”, as described in the Bicentric Pairs section accessible by the Tables button, abbreviates a bicentric pair of points P =\(p : q : r\) and U =\(u : v : w\), where p, q, r have the form g(a,b,c), g(b,c,a), g(c,a,b) and u,v,w have the form h(a,b,c), h(b,c,a), h(c,a,b). “Sum of PU(68)” denotes the point

X₂₅₉₄ (SUM OF PU(68)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2594 = SUM OF PU(68)."""

        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,
            incenter_of,
            nine_point_center_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02594(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2594 = SUM OF PU(68) on reference triangle ABC."""
            X_2594 = eval_trilinear_point(model, A, B, C, '(cos(C- A) + cos(B - A))', ID="X_2594", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            central_line(model, X_1, X_5, 1, 5, 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_59 = eval_trilinear_point(model, A, B, C, '1/(1 - cos(B - C))', ID="X_59", classes=["center", "incident"])
            X_60 = eval_trilinear_point(model, A, B, C, '1/(1 + cos(B - C))', ID="X_60", classes=["center", "incident"])
            central_line(model, X_59, X_60, 59, 60, incident=True)
            return promote_point_to_top(model, X_2594)


        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_2594 on the given reference triangle."""
            model = create_model('X_2594 = SUM OF PU(68)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02594(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-02594.json"))
            write_center_svg(
                model_acute,
                here / "x-02594.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2594¶

X₂₅₉₄¶