← etc / Encyclopedia of Triangle Centers

X₂₈₅₄¶

ISOGONAL CONJUGATE OF X₂₇₇₀

X₂₈₅₄ is the isogonal conjugate of X₂₇₇₀.

X₂₈₅₄ (ISOGONAL CONJUGATE OF X₂₇₇₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2854 = ISOGONAL CONJUGATE OF X_2770."""

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


        def construct_x_02854(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2854 = ISOGONAL CONJUGATE OF X_2770 on reference triangle ABC."""
            X_2770 = eval_barycentric_point(model, A, B, C, '1/(b**(6) + c**(6) - a**(4)*b**(2) - a**(4)*c**(2) + 4*a**(2)*b**(2)*c**(2) - 2*b**(4)*c**(2) - 2*b**(2)*c**(4))', ID="X_2770", classes=["center"])
            X_2854 = isogonal_conjugate(model, A, B, C, X_2770, ID="X_2854", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_6, X_110, 6, 110, incident=True)
            X_67 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(4) + c**(4) - a**(4) - b**(2)*c**(2))', ID="X_67", classes=["center", "incident"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            central_line(model, X_67, X_69, 67, 69, incident=True)
            X_125 = eval_trilinear_point(model, A, B, C, 'cos(A)*(sin(B - C))**(2)', ID="X_125", classes=["center", "incident"])
            X_126 = eval_trilinear_point(model, A, B, C, '(b*c*(2*a**(2) - b**(2) - c**(2))*(b**(4) + c**(4) + a**(2)*(b**(2) + c**(2)) - 4*b**(2)*c**(2)))', ID="X_126", classes=["center", "incident"])
            central_line(model, X_125, X_126, 125, 126, incident=True)
            return promote_point_to_top(model, X_2854)


        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_2854 on the given reference triangle."""
            model = create_model('X_2854 = ISOGONAL CONJUGATE OF X_2770')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02854(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-02854.json"))
            write_center_svg(
                model_acute,
                here / "x-02854.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2854¶

X₂₈₅₄¶