← etc / Encyclopedia of Triangle Centers

X₂₈₃₃¶

ISOGONAL CONJUGATE OF X₂₇₄₉

X₂₈₃₃ is the isogonal conjugate of X₂₇₄₉.

X₂₈₃₃ (ISOGONAL CONJUGATE OF X₂₇₄₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2833 = ISOGONAL CONJUGATE OF X_2749."""

        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,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02833(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2833 = ISOGONAL CONJUGATE OF X_2749 on reference triangle ABC."""
            X_2749 = point_from_barycentrics(model, A, B, C, 1.0214771, 0.072211998, -0.093689089, ID="X_2749", classes=["center"])
            X_2833 = isogonal_conjugate(model, A, B, C, X_2749, ID="X_2833", classes=["selected", "target"])
            X_105 = eval_trilinear_point(model, A, B, C, '1/(b**(2) + c**(2) - a*(b + c))', ID="X_105", classes=["center", "incident"])
            X_107 = eval_trilinear_point(model, A, B, C, '1/(cos(A)*(sin(2*B) - sin(2*C)))', ID="X_107", classes=["center", "incident"])
            central_line(model, X_105, X_107, 105, 107, incident=True)
            X_120 = eval_trilinear_point(model, A, B, C, 'b*c*(2*a*b*c - (b + c)*(a**(2) + (b - c)**(2)))*(b**(2) + c**(2) - a*b -a*c)', ID="X_120", classes=["center", "incident"])
            X_122 = eval_trilinear_point(model, A, B, C, '(b**(2) - c**(2))**(2)*(cos(A) - cos(B)*cos(C))*(cot(A))**(2)', ID="X_122", classes=["center", "incident"])
            central_line(model, X_120, X_122, 120, 122, 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_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            central_line(model, X_30, X_511, 30, 511, incident=True)
            return promote_point_to_top(model, X_2833)


        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_2833 on the given reference triangle."""
            model = create_model('X_2833 = ISOGONAL CONJUGATE OF X_2749')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02833(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-02833.json"))
            write_center_svg(
                model_acute,
                here / "x-02833.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2833¶

X₂₈₃₃¶