← etc / Encyclopedia of Triangle Centers

X₃₅₈₉¶

ISOGONAL CONJUGATE OF X₃₁₀₈

P' = 2u + v + w : u + 2v + w : u + v +2w.

X₃₅₈₉ (ISOGONAL CONJUGATE OF X₃₁₀₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3589 = ISOGONAL CONJUGATE OF X_3108."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            construct_baseline_triangle,
            create_model,
            isogonal_conjugate,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03589(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3589 = ISOGONAL CONJUGATE OF X_3108 on reference triangle ABC."""
            X_3108 = point_from_barycentrics(model, A, B, C, 0.25027168, 0.33323846, 0.41648986, ID="X_3108", classes=["center"])
            X_3589 = isogonal_conjugate(model, A, B, C, X_3108, ID="X_3589", classes=["selected", "target"])
            return promote_point_to_top(model, X_3589)


        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_3589 on the given reference triangle."""
            model = create_model('X_3589 = ISOGONAL CONJUGATE OF X_3108')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03589(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-03589.json"))
            write_center_svg(
                model_acute,
                here / "x-03589.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3589¶

X₃₅₈₉¶