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X₁₉₄₉¶

TRILINEAR POLE OF PU(19)

X₁₉₄₉ = cevapoint of X₁₉₅₀ and X₁₉₅₁

X₁₉₄₉ (TRILINEAR POLE OF PU(19)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1949 = TRILINEAR POLE OF PU(19)."""

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


        def construct_x_01949(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1949 = TRILINEAR POLE OF PU(19) on reference triangle ABC."""
            X_1948 = eval_trilinear_point(model, A, B, C, '(((cos(A))**(2) - cos(B)*cos(C))*csc(2*A))', ID="X_1948", classes=["center"])
            X_1949 = isogonal_conjugate(model, A, B, C, X_1948, ID="X_1949", classes=["selected", "target"])
            X_219 = eval_trilinear_point(model, A, B, C, 'cos(A)*cot(A/2)', ID="X_219", classes=["center", "incident"])
            X_296 = eval_trilinear_point(model, A, B, C, '(cos(A))/((cos(A))**(2) - cos(B)*cos(C))', ID="X_296", classes=["center", "incident"])
            central_line(model, X_219, X_296, 219, 296, incident=True)
            X_108 = eval_trilinear_point(model, A, B, C, 'a/(sec(B) - sec(C))', ID="X_108", classes=["center", "incident"])
            X_1172 = point_from_barycentrics(model, A, B, C, 0.14979394, 0.23060383, 0.61960222, ID="X_1172", classes=["center", "incident"])
            central_line(model, X_108, X_1172, 108, 1172, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_1945 = eval_trilinear_point(model, A, B, C, '(a/((cos(A))**(2) - cos(B)*cos(C)))', ID="X_1945", classes=["center", "incident"])
            central_line(model, X_6, X_1945, 6, 1945, incident=True)
            return promote_point_to_top(model, X_1949)


        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_1949 on the given reference triangle."""
            model = create_model('X_1949 = TRILINEAR POLE OF PU(19)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01949(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-01949.json"))
            write_center_svg(
                model_acute,
                here / "x-01949.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1949¶

X₁₉₄₉¶