← etc / Encyclopedia of Triangle Centers

X₂₁₅₂¶

X₂-ISOCONJUGATE OF X₁₄

X₂₁₅₂ (X₂-ISOCONJUGATE OF X₁₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2152 = X_2-ISOCONJUGATE OF X_14."""

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


        def construct_x_02152(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2152 = X_2-ISOCONJUGATE OF X_14 on reference triangle ABC."""
            X_2152 = eval_trilinear_point(model, A, B, C, 'sin(A)*sin(A -  pi  /3)', ID="X_2152", classes=["selected", "target"])
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            X_48 = eval_trilinear_point(model, A, B, C, 'tan(B) + tan(C)', ID="X_48", classes=["center", "incident"])
            central_line(model, X_31, X_48, 31, 48, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_1094 = eval_trilinear_point(model, A, B, C, '((sin(A +  pi  /3))**(2))', ID="X_1094", classes=["center", "incident"])
            central_line(model, X_1, X_1094, 1, 1094, incident=True)
            X_2154 = eval_trilinear_point(model, A, B, C, '(sin(A)*csc(A -  pi  /3))', ID="X_2154", classes=["center", "incident"])
            X_2173 = eval_trilinear_point(model, A, B, C, 'a*(cos(A) - 2*cos(B)*cos(C))', ID="X_2173", classes=["center", "incident"])
            central_line(model, X_2154, X_2173, 2154, 2173, incident=True)
            return promote_point_to_top(model, X_2152)


        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_2152 on the given reference triangle."""
            model = create_model('X_2152 = X_2-ISOCONJUGATE OF X_14')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02152(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-02152.json"))
            write_center_svg(
                model_acute,
                here / "x-02152.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2152¶

X₂₁₅₂¶