← etc / Encyclopedia of Triangle Centers

X₂₁₆₁¶

X₂-ISOCONJUGATE OF X₃₆

X₂₁₆₁ (X₂-ISOCONJUGATE OF X₃₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2161 = X_2-ISOCONJUGATE OF X_36."""

        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,
            mittenpunkt_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02161(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2161 = X_2-ISOCONJUGATE OF X_36 on reference triangle ABC."""
            X_2161 = eval_trilinear_point(model, A, B, C, '((sin(A))/(1 - 2*cos(A)))', ID="X_2161", classes=["selected", "target"])
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            X_53 = eval_trilinear_point(model, A, B, C, 'tan(A)*cos(B - C)', ID="X_53", classes=["center", "incident"])
            central_line(model, X_19, X_53, 19, 53, incident=True)
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            X_80 = eval_trilinear_point(model, A, B, C, '1/(1 - 2*cos(A))', ID="X_80", classes=["center", "incident"])
            central_line(model, X_9, X_80, 9, 80, incident=True)
            X_45 = eval_trilinear_point(model, A, B, C, '2*b + 2*c - a', ID="X_45", classes=["center", "incident"])
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center", "incident"])
            central_line(model, X_45, X_55, 45, 55, incident=True)
            return promote_point_to_top(model, X_2161)


        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_2161 on the given reference triangle."""
            model = create_model('X_2161 = X_2-ISOCONJUGATE OF X_36')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02161(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-02161.json"))
            write_center_svg(
                model_acute,
                here / "x-02161.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2161¶

X₂₁₆₁¶