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X₂₆₆₇¶

SUM OF PU(85)

X₂₆₆₇ = trilinear pole, wrt incentral triangle, of Lemoine axis

X₂₆₆₇ (SUM OF PU(85)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2667 = SUM OF PU(85)."""

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


        def construct_x_02667(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2667 = SUM OF PU(85) on reference triangle ABC."""
            X_2667 = eval_trilinear_point(model, A, B, C, 'c*a/(c + a) + b*a/(b + a)', ID="X_2667", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            central_line(model, X_1, X_75, 1, 75, incident=True)
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            X_42 = eval_trilinear_point(model, A, B, C, 'a*(b + c)', ID="X_42", classes=["center", "incident"])
            central_line(model, X_37, X_42, 37, 42, incident=True)
            X_192 = eval_trilinear_point(model, A, B, C, 'b*c*(c*a + a*b - b*c)', ID="X_192", classes=["center", "incident"])
            X_714 = eval_trilinear_point(model, A, B, C, '(a **(-4)*(b **(-1) + c **(-1)) - a **(-2)*(b **(-3) + c **(-3)))', ID="X_714", classes=["center", "incident"])
            central_line(model, X_192, X_714, 192, 714, incident=True)
            return promote_point_to_top(model, X_2667)


        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_2667 on the given reference triangle."""
            model = create_model('X_2667 = SUM OF PU(85)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02667(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-02667.json"))
            write_center_svg(
                model_acute,
                here / "x-02667.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2667¶

X₂₆₆₇¶