← etc / Encyclopedia of Triangle Centers

X₈₄₁¶

ISOGONAL CONJUGATE OF X₅₄₁

X₈₄₁ (ISOGONAL CONJUGATE OF X₅₄₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_841 = ISOGONAL CONJUGATE OF X_541."""

        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_00841(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_841 = ISOGONAL CONJUGATE OF X_541 on reference triangle ABC."""
            X_541 = point_from_barycentrics(model, A, B, C, 0.11755139, 0.64096444, -0.75851583, ID="X_541", classes=["center"])
            X_841 = isogonal_conjugate(model, A, B, C, X_541, ID="X_841", classes=["selected", "target"])
            X_376 = eval_trilinear_point(model, A, B, C, '5*cos(A) - cos(B - C)', ID="X_376", classes=["center", "incident"])
            X_476 = eval_trilinear_point(model, A, B, C, '1/((1 + 2*cos(2*A))*sin(B - C))', ID="X_476", classes=["center", "incident"])
            central_line(model, X_376, X_476, 376, 476, incident=True)
            return promote_point_to_top(model, X_841)


        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_841 on the given reference triangle."""
            model = create_model('X_841 = ISOGONAL CONJUGATE OF X_541')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00841(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-00841.json"))
            write_center_svg(
                model_acute,
                here / "x-00841.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X841¶

X₈₄₁¶