← etc / Encyclopedia of Triangle Centers

X₂₄₂₅¶

ISOGONAL CONJUGATE OF X₂₃₉₉

X₂₄₂₅ is the isogonal conjugate of X₂₃₉₉.

X₂₄₂₅ (ISOGONAL CONJUGATE OF X₂₃₉₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2425 = ISOGONAL CONJUGATE OF X_2399."""

        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_02425(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2425 = ISOGONAL CONJUGATE OF X_2399 on reference triangle ABC."""
            X_2399 = point_from_barycentrics(model, A, B, C, -0.98113208, 1.7169811, 0.26415094, ID="X_2399", classes=["center"])
            X_2425 = isogonal_conjugate(model, A, B, C, X_2399, ID="X_2425", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_41 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b + c - a)', ID="X_41", classes=["center", "incident"])
            central_line(model, X_6, X_41, 6, 41, incident=True)
            X_2149 = eval_trilinear_point(model, A, B, C, '(sin(A))/(1 - cos(B - C))', ID="X_2149", classes=["center", "incident"])
            X_2427 = point_from_barycentrics(model, A, B, C, -0.83333333, 0.2, 1.6333333, ID="X_2427", classes=["center", "incident"])
            central_line(model, X_2149, X_2427, 2149, 2427, incident=True)
            return promote_point_to_top(model, X_2425)


        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_2425 on the given reference triangle."""
            model = create_model('X_2425 = ISOGONAL CONJUGATE OF X_2399')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02425(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-02425.json"))
            write_center_svg(
                model_acute,
                here / "x-02425.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2425¶

X₂₄₂₅¶