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X₁₉₈₉¶

ISOGONAL CONJUGATE OF X₃₂₃

X₁₉₈₉ plays a major role in the theory of special isocubics, as presented in Chapter 6 of Jean-Pierre Ehrmann and Bernard Gibert,, “Special Isocubics in the Triangle Plane,” downloadable from Bernard Gibert, Cubics in the Triangle Plane.

X₁₉₈₉ (ISOGONAL CONJUGATE OF X₃₂₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1989 = ISOGONAL CONJUGATE OF X_323."""

        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,
            centroid_of,
            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_01989(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1989 = ISOGONAL CONJUGATE OF X_323 on reference triangle ABC."""
            X_323 = eval_trilinear_point(model, A, B, C, 'sin(3*A)*(csc(A))**(2)', ID="X_323", classes=["center"])
            X_1989 = isogonal_conjugate(model, A, B, C, X_323, ID="X_1989", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_13 = eval_trilinear_point(model, A, B, C, 'csc(A +  pi  /3)', ID="X_13", classes=["center", "incident"])
            central_line(model, X_6, X_13, 6, 13, incident=True)
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_50 = eval_trilinear_point(model, A, B, C, 'sin(3*A)', ID="X_50", classes=["center", "incident"])
            central_line(model, X_30, X_50, 30, 50, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_94 = eval_trilinear_point(model, A, B, C, 'csc(3*A)', ID="X_94", classes=["center", "incident"])
            central_line(model, X_2, X_94, 2, 94, incident=True)
            return promote_point_to_top(model, X_1989)


        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_1989 on the given reference triangle."""
            model = create_model('X_1989 = ISOGONAL CONJUGATE OF X_323')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01989(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-01989.json"))
            write_center_svg(
                model_acute,
                here / "x-01989.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1989¶

X₁₉₈₉¶