← etc / Encyclopedia of Triangle Centers

X₁₉₆₈¶

CROSSSUM OF PU(37)

X₁₉₆₈ (CROSSSUM OF PU(37)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1968 = CROSSSUM OF PU(37)."""

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


        def construct_x_01968(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1968 = CROSSSUM OF PU(37) on reference triangle ABC."""
            X_1968 = eval_trilinear_point(model, A, B, C, 'a*((tan(A))**(2) + tan(B)*tan(C))', ID="X_1968", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", classes=["center", "incident"])
            central_line(model, X_4, X_32, 4, 32, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_64 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - cos(B)*cos(C))', ID="X_64", classes=["center", "incident"])
            central_line(model, X_6, X_64, 6, 64, incident=True)
            X_33 = eval_trilinear_point(model, A, B, C, '1 + sec(A)', ID="X_33", classes=["center", "incident"])
            X_172 = eval_trilinear_point(model, A, B, C, 'a**(3) + a*b*c', ID="X_172", classes=["center", "incident"])
            central_line(model, X_33, X_172, 33, 172, incident=True)
            return promote_point_to_top(model, X_1968)


        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_1968 on the given reference triangle."""
            model = create_model('X_1968 = CROSSSUM OF PU(37)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01968(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-01968.json"))
            write_center_svg(
                model_acute,
                here / "x-01968.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1968¶

X₁₉₆₈¶