← etc / Encyclopedia of Triangle Centers

X₂₆₆₃¶

CROSSSUM OF PU(84)

X₂₆₆₃ (CROSSSUM OF PU(84)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2663 = CROSSSUM OF PU(84)."""

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


        def construct_x_02663(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2663 = CROSSSUM OF PU(84) on reference triangle ABC."""
            X_2663 = eval_trilinear_point(model, A, B, C, '((1/a + 1/b)*(1/a + 1/c) + (1/b + 1/c)**(2))', ID="X_2663", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_1, X_6, 1, 6, incident=True)
            X_42 = eval_trilinear_point(model, A, B, C, 'a*(b + c)', ID="X_42", classes=["center", "incident"])
            X_894 = eval_trilinear_point(model, A, B, C, '(a**(2) + b*c)/a', ID="X_894", classes=["center", "incident"])
            central_line(model, X_42, X_894, 42, 894, incident=True)
            X_86 = eval_trilinear_point(model, A, B, C, 'b*c/(b + c)', ID="X_86", classes=["center", "incident"])
            X_872 = eval_trilinear_point(model, A, B, C, '(a*(b + c))**(2)', ID="X_872", classes=["center", "incident"])
            central_line(model, X_86, X_872, 86, 872, incident=True)
            return promote_point_to_top(model, X_2663)


        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_2663 on the given reference triangle."""
            model = create_model('X_2663 = CROSSSUM OF PU(84)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02663(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-02663.json"))
            write_center_svg(
                model_acute,
                here / "x-02663.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2663¶

X₂₆₆₃¶