← etc / Encyclopedia of Triangle Centers

X₁₉₄₁¶

CROSSSUM OF PU(17)

X₁₉₄₁ (CROSSSUM OF PU(17)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1941 = CROSSSUM OF PU(17)."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01941(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1941 = CROSSSUM OF PU(17) on reference triangle ABC."""
            X_1941 = eval_trilinear_point(model, A, B, C, '(cos(B)*cos(C)*((cos(A))**(4) + (cos(B))**(2)*(cos(C))**(2)))', ID="X_1941", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_155 = eval_trilinear_point(model, A, B, C, '(cos(A))*((cos(B))**(2) + (cos(C))**(2) - (cos(A))**(2))', ID="X_155", classes=["center", "incident"])
            central_line(model, X_4, X_155, 4, 155, incident=True)
            X_185 = eval_trilinear_point(model, A, B, C, '(cos(A))*(1 - cos(A)*cos(B - C))', ID="X_185", classes=["center", "incident"])
            X_648 = eval_trilinear_point(model, A, B, C, '1/(a*(b**(2) - c**(2))*(b**(2) + c**(2) - a**(2)))', ID="X_648", classes=["center", "incident"])
            central_line(model, X_185, X_648, 185, 648, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_1075 = eval_trilinear_point(model, A, B, C, '(sec(A))*((sec(B))**(2) + (sec(C))**(2) - (sec(A))**(2))', ID="X_1075", classes=["center", "incident"])
            central_line(model, X_3, X_1075, 3, 1075, incident=True)
            return promote_point_to_top(model, X_1941)


        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_1941 on the given reference triangle."""
            model = create_model('X_1941 = CROSSSUM OF PU(17)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01941(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-01941.json"))
            write_center_svg(
                model_acute,
                here / "x-01941.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1941¶

X₁₉₄₁¶