← etc / Encyclopedia of Triangle Centers

X₂₆₀₁¶

CROSSSUM OF PU(69)

X₂₆₀₁ (CROSSSUM OF PU(69)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2601 = CROSSSUM 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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            nine_point_center_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02601(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2601 = CROSSSUM OF PU(69) on reference triangle ABC."""
            X_2601 = eval_trilinear_point(model, A, B, C, 'sec(A - B)*sec(A - C) + (sec(B - C))**(2)', ID="X_2601", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_2120 = point_from_barycentrics(model, A, B, C, 0.30475192, 0.22664215, 0.46860594, ID="X_2120", classes=["center", "incident"])
            central_line(model, X_1, X_2120, 1, 2120, incident=True)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_2602 = eval_trilinear_point(model, A, B, C, 'sec(A - B)*sec(A - C) - (sec(B - C))**(2)', ID="X_2602", classes=["center", "incident"])
            central_line(model, X_5, X_2602, 5, 2602, incident=True)
            X_2594 = eval_trilinear_point(model, A, B, C, '(cos(C- A) + cos(B - A))', ID="X_2594", classes=["center", "incident"])
            X_2603 = eval_trilinear_point(model, A, B, C, '(1/(sec(A - B)*sec(A - C) - (sec(B - C))**(2)))', ID="X_2603", classes=["center", "incident"])
            central_line(model, X_2594, X_2603, 2594, 2603, incident=True)
            return promote_point_to_top(model, X_2601)


        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_2601 on the given reference triangle."""
            model = create_model('X_2601 = CROSSSUM OF PU(69)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02601(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-02601.json"))
            write_center_svg(
                model_acute,
                here / "x-02601.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2601¶

X₂₆₀₁¶