← etc / Encyclopedia of Triangle Centers

X₁₉₂₂¶

TRILINEAR POLE OF PU(12)

X₁₉₂₂ = perspector of ABC and unary cofactor triangle of Gemini triangle 31

X₁₉₂₂ (TRILINEAR POLE OF PU(12)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1922 = TRILINEAR POLE OF PU(12)."""

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


        def construct_x_01922(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1922 = TRILINEAR POLE OF PU(12) on reference triangle ABC."""
            X_1921 = eval_trilinear_point(model, A, B, C, '(b**(3)*c**(3)*(a**(2) - b*c))', ID="X_1921", classes=["center"])
            X_1922 = isogonal_conjugate(model, A, B, C, X_1921, ID="X_1922", classes=["selected", "target"])
            X_58 = eval_trilinear_point(model, A, B, C, 'a/(b + c)', ID="X_58", classes=["center", "incident"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            central_line(model, X_58, X_101, 58, 101, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_291 = eval_trilinear_point(model, A, B, C, '1/(a**(2) - b*c)', ID="X_291", classes=["center", "incident"])
            central_line(model, X_6, X_291, 6, 291, incident=True)
            X_81 = eval_trilinear_point(model, A, B, C, '1/(b + c)', ID="X_81", classes=["center", "incident"])
            X_335 = eval_trilinear_point(model, A, B, C, 'b*c/(a**(2) - b*c)', ID="X_335", classes=["center", "incident"])
            central_line(model, X_81, X_335, 81, 335, incident=True)
            return promote_point_to_top(model, X_1922)


        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_1922 on the given reference triangle."""
            model = create_model('X_1922 = TRILINEAR POLE OF PU(12)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01922(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-01922.json"))
            write_center_svg(
                model_acute,
                here / "x-01922.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1922¶

X₁₉₂₂¶